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THE ELEMENTS OF 
ELECTRICITY 



BY 

WIRT ROBINSON 

COTONEL, UNITED STATES ARMY, PROFESSOR 

OF CHEMISTRY, ETC., UNITED STATES 

MILITARY ACADEMY 



THIRD EDITION, REVISED 



NEW YORK 

JOHN WILEY & SONS, Inc. 

London: CHAPMAN & HALL, Limited 
1922 







Copyright, 1914, 1922 

BY 

WIRT ROBINSON 



Stanbope jpress 

F. H.GILSON COMPANY 
BOSTON, U.S.A. 



£& AUG 19 1922 



ICI.A677919 



6-22 



PREFACE. 



The following text book on electricity has been prepared for 
use of the Cadets of the United States Military Academy. 

The course being required of all members of the third year 
class, explanations have been given in more detail than would be 
necessary were it elective. Recitations on the text proper are 
accompanied by the solution of numerous problems and class room 
instruction is supplemented by from eight to ten lectures and 
twenty laboratory periods. 

WIRT ROBINSON. 

West Point, New York. 
December 18, 1913. 



PREFACE TO THIRD EDITION. 

In the present edition, certain changes which an experience 
of ten years use of the book in the class room has shown to be 
advisable, and other changes rendered necessary by the develop- 
ment of the science, have been made. 



WIRT ROBINSON. 



West Point, New York. 
March 8, 1922. 



in 



TABLE OF CONTENTS. 



INTRODUCTORY. 



CHAPTER 1. 
Units. 

Page 

Need of Units — Fundamental Units — Standard of Length — Metric System 

— Units of Mass and Time — C. G. S. System — Absolute Units 1 

CHAPTER 2. 
Electricity. 

Origin of Name — Divisions of Subject 6 

PART I. 
STATIC ELECTRICITY. 

CHAPTER 3. 

Electric Attraction and Repulsion. 

Electric Attraction — Electric Charge — Conductors and Non-Conductors — 
All Bodies Susceptible of Electrification — Electric Repulsion — Two 
Kinds of Electrification — Simultaneous Production of Equal Amounts 
— Electroscopes — Theories of Electricity 9 

CHAPTER 4. 

Electrostatic Induction. 

Electrification by Influence — Distribution of Induced Charge — Attraction 
and Repulsion Explained — Amount of Induced Charge — Separation 
of Induced Charges — Free and Bound Charges — Gold Leaf Electro- 
scope — Electrophorus 17 

CHAPTER 5. 

Distribution of Charge. 

Charge on Non-Conductor — On Conductor— Confined to Surface — Plot's 
Experiment — Distribution of Charge — Surface Density — Effect of 
Points — Franklin's Experiment — Other Experiments — Division of 
Charge 24 



VI TABLE OF CONTEXTS. 

Page 

CHAPTER 6. 

Electrical Machines. 

Kinds — Frictional Machines — Cylinder Machine — Toepler's Machine — 

Holtz's Machine — Electrical Diagrams 30 

CHAPTER 7. 

Laws of Electric Attraction and Repulsion. 

Coulomb's Torsion Balance — Law of Inverse Squares — Variation of Force 
with Charges — with Intervening Medium — Unit Quantity of Elec- 
tricity 37 

CHAPTER 8. 

Electric Field. 

Electric Field — Intensity — Direction — Lines of Force — Graphic Represen- 
tation of Field — Tubes of Force — Lines from Unit Charge — Gauss' 
Theorem — Field about Uniformly-Charged Sphere — near Uniformly- 
Charged Plane — Force Exerted upon Internal Point by Uniformly- 
Charged Sphere — Charge Resides on Surface 43 

CHAPTER 9. 

Potential. 

Cause of Movement of Electric Charges — Physical Analogues of Electric 
Potential — Mechanical Potential — Electric Potential — Zero Potential 
— Potential at Point Due to a Charge — Expression for Electric Force 
— Electromotive Force — Practical Unit of E. M. F. — Summary 51 

CHAPTER 10. 

Electrostatic Capacity. 

Electrostatic Capacity — Capacity of Sphere — Case of Two United Spheres 
— of Two Coalescing Spheres — Condensers — Invention of Leyden Jar 
— Explanation of Leyden Jar — Location of Charge of Condenser — 
Capacity of Spherical Condenser — of Plate Condenser — Dielectric 
Capacity — Determination — Dielectric Capacity of Various Sub- 
stances — Dielectric Strength — Commercial Condensers — Practical 
Unit of Capacity — Work Expended in Charging a Condenser — Energy 
of a Condenser 59 

CHAPTER 11. 

Electrostatic Measurements. 

Electrostatic Measurements — Unit Jars — Principle of Electrometers — 

Attracted Disc Electrometer — Quadrant Electrometer 77 



TABLE OF CONTENTS. Vll 

Page 
PART II. 

MAGNETISM. 

CHAPTER 12. 

Magnets. 

Natural Magnets — Lodestones — Fables of Ancients — Doctor Gilbert — 
Artificial Magnets — Magnetic Poles — Poles Inseparable — Magnetic 
Attraction — Mutual Action of Magnets — Why Needle Points North 
and South — Poles Misnamed — Magnetization by Induction — Induc- 
tion — Induction Takes Place through Space — Magnetic Attraction 
Explained — Other Magnetic Substances — Diamagnetism 85 

CHAPTER 13. 
Measurement of Magnetic Forces. 

Coulomb's First Law — Lifting Power of Magnets — Strength of Magnets — 
Magnetic Pole Defined — Measurement of Magnetic Forces — Cou- 
lomb's Second Law — Method by Oscillations — Magnetic Moment — 
Experimental Proof of Law of Inverse Squares — Unit Magnetic Pole . 93 

CHAPTER 14. 
The Magnetic Field. 

Magnetic Field — Direction — Intensity— Magnetic Lines of Force — Map- 
ping Lines of Force — Permanent Record of Magnetic Figures — Com- 
pounding Magnetic Fields — Properties of Magnetic Lines of Force — 
Magnetic Lines Pass Preferably through Magnetic Substances — Law 
of Maximum Flux — Graphic Representation of Intensity of Magnetic 
Field — Comparison of Magnetic Fields — Tangent Law — Sine Law — 
Determination of Strength of Magnetic Field — Turning Moment of 
Magnets 101 

CHAPTER 15. 
Theory of Magnetism. 

Magnetism — Molecular Magnetism — Ewing's Theory — Magnetization Ac- 
companied by Molecular Movement — Effect of Vibration — Effect of 
Heat— Effect of Solution 118 

CHAPTER 16. 
Manufacture of Magnets. 

Most Suitable Metal — Principle of Manufacture — Method by Single 
Touch — Divided Touch — Magnetization by Electric Current — Con- 
sequent Poles — Magnetization Confined to Outer Layers — Aging of 
Magnets 123 



Vlll TABLE OF CONTENTS. 

Page 
CHAPTER 17. 

Terrestrial Magnetism. 

Location of Earth's Magnetic Poles — Magnetic Declination — Isogonic 
Chart — Magnetic Dip — Dipping Needle — Isoclinic Chart — Magnetic 
Intensity — Magnetic Elements — Variations — Secular Change in Dec- 
lination and Dip — Diurnal Change in Declination — Annual Change 
in Declination — Magnetic Storms — Theories of Earth's Magnetism — 
Mariner's Compass — Adjustments 127 

PART m. 
VOLTAIC ELECTRICITY. 

CHAPTER 18. 

Discoveries of Galvani and Volta. 

Galvani's Discovery — Volta's Investigations — Volta's Contact Series — 
Contact Theory — Later Theory — Voltaic Pile — Circlet of Cups — 
Source of Electrical Energy 145 

CHAPTER 19. 

The Simple Cell. 

Simple Voltaic Cell — Material Used for Elements — Chemical Action — 
Local Action — Remedy — Polarization — Depolarizers — Requirements 
of a Voltaic Cell 154 

CHAPTER 20. 
Kinds of Cells. 

Great Variety of Cells — Classification — Grove — Bunsen — Bichromate — 
Daniell — Gravity — Edison-Lalande — Leclanche — Dry Cells — Need of 
Standard Cells — Clark's Cell — Weston's Standard Cell — Conven- 
tional Sign for Cell 160 

CHAPTER 21. 
The Electric Current and Its Chemical Action. 

Electric Current — No Current unless Circuit Complete — Direction of 
Flow — Decomposition of Water — Electrolysis of Water — Faraday's 
Terminology — Substances Subject to Electrolysis— Electrolysis of 
Fused Compound — of a Base — of a Metallic Salt — Electro-Chemical 
Classification of Elements — Faraday's First Law — Voltameter — The 
Coulomb and Ampere — Equality of Current at Every Cross-Section — 
Corollary — Faraday's Second Law — Electro-Chemical Equivalent — 
Definition of Ampere in Terms of Silver — Applications of Electrolysis 
— Refining of Copper — Electroplating — Electrotyping 170 



TABLE OF CONTENTS. IX 

Page 

CHAPTER 22. 

The Storage Battery. 

Reversibility of Cells — Storage Battery — Elements of a Secondary Cell — 
Preparation of Plates — Plante Cell — Chloride Accumulator — Shape 
and Size of Plates — Grouping of Plates — Reactions — Charging — 
Indications of Charge — Troubles of Lead Batteries — Care — Objections 
— Edison Storage Battery — Reactions — Charging — Advantages and 
Disadvantages — Use of Storage Batteries 182 

CHAPTER 23. 

Theory of Electrolytic Dissociation. 

Interdependence of Physical Sciences — Laws of Variation of Gaseous 
Pressure — Decomposition and Dissociation — Example of Dissociation 
by Heat — Osmosis and Osmotic Pressure — Demonstration — Measure- 
ment of Osmotic Pressure — Observations of Pfeffer — Osmotic Pressure 
Follows Laws of Gaseous Pressure — Van't Hoff's Generalization — 
Exceptions — Dissociation Theory of Arrhenius — Why Ionization 
Takes Place in Solutions — How Ionization Takes Place — Ionization 
Incomplete — Demonstration of Free Ions — Ions not from Same Mole- 
cule — Grotthus' Theory — Electrolytes and Non-Electrolytes — Elec- 
trolytic Properties Depend upon Ionization — Vapor Tension — Solution 
Tension — Theory Applied to Simple Cell — Atomic Character of Elec- 
tricity — Scope of Theory 198 



CHAPTER 24. 

Resistance. 

Resistance — Example of Effect — Practical Unit — The Ohm — Laws of 
Resistance — Variation with Length — with Cross-Section — Specific 
Resistance — Variation with Temperature — Platinum Thermometer — 
Ohm Defined in Terms of Column of Mercury — Resistance and Con- 
ductance — Resistance of Conductors in Parallel — Internal Resistance 
of Cells — Wire Tables — Circular Measure of Wires 213 



CHAPTER 25. 

Ohm's Law. 

Ohm's Law — Drop of Potential — Law Applies to Any Portion of Circuit — 
Division of Current in Divided Circuit — Shunts — Rheostats — Kir- 
choff's Laws— Lost and Useful Volts — Short Circuit — Definitions 
Based on Ohm's Law 223 



X TABLE OF CONTENTS. 

Page 

CHAPTER 26. 

Measurement of Resistance. 

Measurement of Resistance — Drop of Potential Proportional to Resistance 
— Measurement by Drop of Potential — Resistance Coils — Drop in 
Divided Circuit — Principle of Wheatstone Bridge — Arrangement of 
Resistances — Evolution in Form — Operation of Measurement — 
Bracketing — Order of Closing Keys — Ratio to Use — Bridge with Re- 
versible Ratios— Dial Bridge — Resistances that may be Measured — 
Slide Wire Bridge — Measurement of High Resistance — Resistance of 
Electrolytes — Internal Resistance of Cells 233 

CHAPTER 27. 

The Potentiometer. 

Measurement of E. M. F. of Cells — Preliminary Arrangement of Poten- 
tiometer — Calibration — Measurement 248 

CHAPTER 28. 

Grouping of Cells in Batteries. 

Grouping of Cells — in Series — in Parallel — Comparison of Two Groupings 
— Analogy between Cells and Pumps — Multiple Grouping — Maximum 
Current — Diagrams — Cost of Power from Primary Cells 251 

PART IV. 

ELECTRO-MAGNETICS. 

CHAPTER 29. 
Magnetic Field About a Wire Carrying a Current. 

Oerstedt's Discovery — Right Hand Rule for Deflection of Needle — Mag- 
netic Field about Wire — Direction — Clock Rule — Wire Carrying a 
Current is not a Magnet — Rotation of Magnetic Pole by Current — of 
Current by Pole — Left Hand Rule for Direction of Motion — Intensity 
of Field about Straight Conductor — Field on Axis of Circular Coil — 
Absolute Unit of Current — Force Exerted by Magnetic Field upon 
Conductor Carrying a Current — Work Done in Moving across a Field 
a Conductor Carrying a Current — Energy Expended on an Electro- 
Magnetic Field — Force between Parallel Conductors Carrying Cur- 
rents 259 

CHAPTER 30. 

Galvanoscopes and Galvanometers. 

Galvanoscopes — Increase of Sensitiveness — Schweigger's Multiplier — 
Methods of Weakening Controlling Force — Haiiy's Method — Astatic 
Combinations — Magnetic Shells — De La Rive's Battery — Maxwell's 



TABLE OF CONTENTS. XI 

Page 

Law — Galvanometers — Tangent Galvanometer — Measurement of 
Current by Tangent Galvanometer — Sine Galvanometer — Mirror 
Galvanometer — Suspended Coil Galvanometer — Damping — Galvan- 
ometer Shunts — Universal Shunt — Weber's Electro-Dynamometer — 
Siemen's Electro-Dynamometer — Ballistic Galvanometer 274 

CHAPTER 31. 

Electric Magnetization of Iron and Steel. 

Solenoid — Equivalent to Bar Magnet — Intensity of Field on Axis — Am- 
pere Turns — Variation of Field with Current — Effect of Material of 
Core on Field — Permeability — Magnetic Saturation — Curves of Mag- 
netization — Ewing's Theory of Molecular Magnetism — Hysteresis — 
Cycle of Magnetization — Energy Loss due to Hysteresis — Law of 
Magnetic Circuit — Calculation of Flux — Diamagnetism 295 

CHAPTER 32. 

Electro-Magnets. 

Electro-Magnets — Rules for Polarity — Value of Electro-Magnets — Trac- 
tive Power — Shape — Use — Lifting Weights — Electric Bells — Tele- 
graph — Morse Telegraph — American System — Overload Switch — 
Underload Switch 310 

CHAPTER 33. 

Induction. 

Faraday's Discovery of Induction — Faraday's Second Discovery — Inertia 
of Electro-Magnetic Fields — Explanation Applied to Magnet and 
Coil— to Two Coils— Rule for Direction of Induced E. M. F.— Right 
Hand Rule — Mechanical Production of Electric Current — Cutting of 
Lines of Force — Relation between Rate of Cutting and Resulting E. 
M. F— Absolute Electro-Magnetic Unit of E. M. F.— Practical Unit 
of E. M. F., the Volt — Eddy Currents — Foucault's Experiments — 
Lenz's Law — Transformers — Self-Induction — Measure — Inductance 
— Expression for Inductance of Coil — Helmholtz's Equation — Induced 
E. M. F. at Make and Break — Induction Coil — Use of Condenser — 
Bell Telephone — Transmitter — Operation of Telephone 321 

CHAPTER 34. 

Ammeters and Voltmeters. 

Electrical Quantities to be Measured — Effects Used in Measurements — 
Effect Best Adapted for Measurement — Electro-Chemical Effect Se- 
lected — Why Silver Selected — Reason for Weight — Electro-Chemical 
Effect Unsuitable for Industrial Needs — Electro-Magnetic Effect 



Xll TABLE OF CONTENTS. 

Page 

best for Practical Measurements — Calibration of Galvanometer — 
Difference between Ammeters and Voltmeters — Ammeters — Voltmeter 
between Two Points of a Circuit — E. M. F. of a Cell or Battery — 
Classification of Ammeters and Voltmeters — Hot Wire Instruments — 
Moving Iron Instruments — Switchboard Shunts — Weston D. C. Am- 
meter — Weston D. C. Voltmeter — Multipliers — Weston D. C. A. C. 
Voltmeter — Thomson Inclined Coil Instruments — Use of Transform- 
ers with A. C. Instruments — Milli voltmeters — Milli voltmeters as 
Ammeters — Millivoltmeter Shunt 349 

CHAPTER 35. 

Heating Effect of Electric Current. 

Work done by Electric Current — Determination of Laws of Heating Effect 
— The Joule — Theoretical Deduction of Joule's Law — Electric Heating 
of Wires — Calculation of Temperature — Localizing the Heating Effect 
— Electric Fuzes — Electric Welding — Electric Arc — Electric Furnace 
— Moissan's Furnace — Manufacture of Carborundum — Manufacture 
of Aluminum — Electric Iron Furnaces — The Induction Furnace 376 

CHAPTER 36. 

Electric Power. 

Power Defined — Horse Power — Expression for Electric Power — Develop- 
ment of Power in a Battery — Units of Electric Power — Measurement 
of Power by Electro-Dynamometer — Indicating Wattmeter — Integrat- 
ing Wattmeter — Electrical Transmission of Power — Considerations 
Affecting Electrical Transmission of Power 387 

CHAPTER 37. 

Electric Lighting. 

The Electric Light — Incandescent Lamp — Carbon Filament — Manufacture 
of the Lamp — Recent Incandescent Lamps — Nernst Lamp — Candle 
Power — Photometry — Life of Incandescent Lamp — Efficiency — Con- 
trol of Light — Grouping of Incandescent Lamps — Arc Light — Car- 
bons — Requirements of Arc Light Mechanism — Clutch — Constant 
Potential Arc Lamp — Constant Current Arc Lamp — Enclosed Arc- 
Flaming Arc — Magnetite Arc Lamp — Efficiency of Arc Lights — 
Luminous Vapor Lamps — The Moore Light — Cooper-Hewitt Mercury 
Vapor Lamp 397 

CHAPTER 38. 

T hermo-Electrics. 

Seebeck's Discoveries — Thermo-Electric Inversion — The Peltier Effect — 

Thomson Effect — Thermopile — Radiometer — Radio-Micrometer. . . . 416 



TABLE OF CONTENTS. xiii 

Page 

CHAPTER 39. 
Remarks on Certain Electric Units. 

Two Systems of Electric Units — Units of Current and Quantity — Units of 
Electro-Motive Force — Primary Electro-Magnetic Units — -Dimen- 
sional Formulae — Dimensional Formula of Electro-Magnetic Resist- 
ance — Resistance Expressed as Velocity — Absolute Measurement of 
Resistance — The Ohm — The Ampere — The Volt — Resume — Compari- 
son of the dimensional Formulae in the Two Systems — Explanation 
of Lack of Agreement 423 



PART V. 
ELECTRO-MECHANICS. 

CHAPTER 40. 
Direct Current Generators. 

Electro-Mechanics — Classes of Electrical Machines — Coil Rotating in a 
Magnetic Field — Calculation of E. M. F. of Rotating Coil — Produc- 
tion of Current by Rotating Coil — Alternating Current — Graphic 
Representation of Alternating E. M. F. and Current— Rectification of 
Alternating Current — Increase in Number of Turns of Coil — Increase 
in number of Coils — Open and Closed Coils — Essential parts of D. C. 
Generator — The Field — Excitation of Field Magnets — -Methods of 
Self-Excitation — Control of Field — Armature Core — Classes of Arma- 
tures — The Commutator — Brushes — Ring-Wound Generator- — Arma- 
ture Reaction — Commutation — Sparking — Multipolar Generators — 
Advantages of Multipolar Generators — Drum Windings — Plane De- 
velopment of Drum- Winding — Star Development of Drum- Winding — 
Calculation of E. M. F. of Generator — Switchboards — Example of 
Switchboard — Coupling of Generators; Three- Wire System 433 

CHAPTER 41. 
Generator Characteristics. 

Adaptation of Generator to Work Required — Characteristics — Magneti- 
zation Characteristic — Characteristic of Series Generator — Critical 
Resistance — Characteristic of Shunt Generator — Compound Gener- 
ator — Over-Compounding 466 

CHAPTER 42. 

Direct Current Motors. 

The Motor and the Generator Identical — Explanation of Motion — Power 
Developed by a Motor — Counter Electro-Motive Force — Relation Be- 
tween Counter E. M. F. and Power Developed — Reading of Voltmeter 
Across Seat of Counter E. M. F. — Efficiency of Motors — Maximum 



xiv TABLE OF CONTENTS. 

Page 

Output of Power — Classes of D. C. Motors — The Shunt Motor — 
Control of Speed of Shunt Motors — Starting Box for Shunt Motors — 
Series Motors — Speed of Series Motors — Change of Direction of 
Rotation — Motor-Generators 474 



CHAPTER 43. 

Alternating Currents. 

Alternating E. M. F. and Current — Why Considered Separately — Cycle, 
Period and Frequency — Phase — Vector Diagrams — Composition of 
Alternating E. M. F.s— Value of an Alternating Current — Self Induc- 
tion — Inductance — Inductance and Resistance — Alternating E. M. F. 
in a Circuit having Resistance and Inductance — Graphic Construction 
of E. M. F. and Current Curves — Inductive Reactance — Impedance — 
Choke Coils — Explanation of Operation of Choke Coils — Inductance 
and Resistance in Series — Inductance and Resistance in Parallel — 
Capacity — Condenser in an Alternating Current Circuit — E. M. F. 
and Current Curves in Case of Capacity — Capacity Reactance — ■ 
Alternating E. M. F. in Circuit containing Resistance, Inductance 
and Capacity — Electric Resonance — Resonance with Inductance and 
Capacity in Series — Resonance with Inductance and Capacity in 
Parallel — Power in an Alternating Current Circuit — Power Factor. . 488 



CHAPTER 44. 

Alternating Current Generators. 

Alternators — Field Excitation of Alternators — Compound Alternators — 
Alternators Usually Multipolar — Classes of Alternators — Alternators 
with Revolving Armatures — Alternators with Revolving Field — The 
Inductor Alternator — Polyphase Alternators — Tri-Phase Alternators 
— Tri-Phase Delta-Connection — Tri-Phase Y-connection — Trans- 
formation of Direct and of Alternating Currents — Transformers — 
Operation of Transformer — Connection of Transformers — Auto-Trans- 
formers — Rectification of Alternating Current — The Mercury Arc 
Rectifier — Rectification of Single-Phase Current — Comparison of 
Alternating and Direct Currents 515 



CHAPTER 45. 

Alternating Current Motors. 

Alternating Current Motors — Classes of A. C. Motors — Series Motors — 
Synchronous Motors — Operation of Synchronous Motors — The Re- 
pulsion Motor — Principle of Induction Motor — Production of Rotat- 
ing Field — The Induction Motor 533 



TABLE OF CONTENTS. XV 

Page 

PART VI. 
HIGH POTENTIAL. 

CHAPTER 46. 

Discharge of Electricity Through Gases. 

High Potential — Conductivity of Gases — Discharge Through Moderate 
Vacua — Effect of Magnetic Field on Positive Column— Discharge 
Through High Vacua — Cathode Rays — Nature of Cathode Rays — 
Effect of Magnetic Field on Cathode 'Rays — Effect of Electric Field 
upon Cathode Rays — Nature of Charge Carried by Corpuscles — 
Positive Rays — Lenard Rays — X-Rays — Becquerel Rays — Increase 
of Conductivity of Gases — Ionization of Gases — Investigation of 
Corpuscles — Velocity of Corpuscles — Mass of Corpuscle — Nature of 
Corpuscles 543 

CHAPTER 47. 

Electric Oscillations. 

Henry's Theory of Oscillatory Discharge of Leyden Jar — Thomson's Math- 
ematical Proof of Oscillation — Feddersen's Experiment with Revolving 
Mirror — Explanation of Oscillation — Maxwell's Electro-Magnetic 
Theory — Electric Elasticity — Electric Density — Velocity of Propaga- 
tion of Electric Wave — Hertz's Confirmation of Maxwell's Theory — 
Further Experiments by Hertz — Length of Electro-Magnetic Waves — 
Tuning of the Resonator — Principle of Wireless Telegraphy — The 
Aerial — The Transmitter — Coupled Circuits — Tuning of Coupled Cir- 
cuits — Branley's Coherer — Operation of Receiving Circuit — Use of 
Telephone and Detectors — The Vacuum Tube 556 



INTRODUCTORY. 



CHAPTER 1. 
UNITS. 



1. Need of Units. — In the orderly study of any concrete 
science we early encounter the necessity for dealing with quanti- 
ties. Quantities may be specified and an accurate conception of 
them conveyed to others only by stating how many times greater 
or less they are than some like quantity of which there is common 
knowledge. Those quantities employed as bases of comparison 
are called units. 

2. Electrical Units to be Defined Later. — In beginning a study 
it might seem logical that we should first define the units to be 
used, but in electricity the number of units is perhaps greater than 
in any other one branch of science and a preliminary definition 
of them would from their mere number tend to confusion rather 
than to clearness; moreover, an accurate conception of some of 
them requires more or less knowledge of certain electrical principles 
and relations, therefore, it is found best to reserve these definitions 
until, in the development of the subject, the necessity for their 
use arises. 

3. Fundamental Units. — There are, however, certain units of 
general application in all sciences and of these it is well to have 
from the beginning a definite conception. Such are the so-called 
"fundamental" units of length, mass and time and some others 
derived from these. 

We may, in a sense, regard the unit of length alone as the fun- 
damental unit for it is possible to define all the others more or less 
directly by reference to length. Thus, the unit of mass may be 
denned as the mass of water under certain conditions contained 
in a cube of certain dimensions, the unit of time in terms of the 
period of oscillation at a certain locality of a pendulum of a cer- 
tain length, the unit of heat in terms of the linear expansion of 
mercury, etc. 

1 



2 ELEMENTS OF ELECTRICITY. 

The term ' 'fundamental" is however applied to the units of 
length, mass and time because in addition to the simpler derived 
units of area, volume and weight, it is possible, as will be shown 
below, to express all such dynamical quantities as velocity, force, 
work, etc., in terms of these units. This does not mean that there 
is one universal fundamental unit of length or of mass or of time. 
The units are chosen arbitrarily, but once having been selected 
the system of derived units follows. 

4. Standard of Length. — The desirability of having a single 
unvarying standard of length, one that could be reproduced should 
existing standards be destroyed, has long been evident. It has 
been proposed to take as such standard the length of the simple 
seconds pendulum at the sea level at some definite locality. This 
is about 39.14 inches. 

The French government caused to be made most accurate meas- 
urements of several meridian arcs of the earth's surface whence 
was calculated the length of the meridian quadrant through Paris 
and one ten-millionth part of this quadrant (about 40 inches) 
was adopted as the measure of length and hence called the meter. 
A standard meter of platinum was made and is preserved in 
France. It is now known that an error was made in the deter- 
mination of the length of the quadrant and that it is some 880 
meters longer, so that practically the meter is the length of the 
platinum bar, the ''metre des archives 1 ' of France. Its length is 
39.37+ inches. 

5. Need of Multiples and Submultiples. — Although it would 
seem that there should be but one unit for any one kind of quan- 
tity, as a matter of fact this is not the case. The need of more 
than one arises mainly from the fact that the average human 
mind can not form a direct concrete conception of a quantity 
expressed by more than three figures. For example, should a 
person say that he had walked 63,360 inches we have no precise 
image of the actual distance, and even when expressed as 5280 
feet we involuntarily translate into the next higher unit; but when 
he says that he has walked one mile we get a definite idea. In the 
other direction, to speak of an object as one 63,360th of a mile thick 
is almost meaningless but one inch conveys the exact impression. 
Therefore in practical affairs we require large units to measure 
large quantities and small units to measure small quantities. 



INTRODUCTORY. 6 

6. The Metric System. — It is not necessary to explain here 
the advantages of the metric or decimal system. The following 
table of English measures of length — 

3 barleycorns make an inch 
12 inches make a foot 

3 feet make a yard 
1760 yards make a mile 
and the fact that besides these we have the line, the hand, the 
ell, the fathom, the rod, perch or pole, the chain, the furlong, the 
geographical mile, the nautical mile, the knot, the league, etc., 
between which in general no interrelation exists, are sufficient to 
show how illogical is our system. This is brought out all the 
more forcibly when we attempt to pass from one of these units to 
another or to make a calculation in which several are involved or 
to pass from linear dimensions to measures of capacity. 

The metric system has by act of Congress been formally 
legalized for use in this country, but in spite of its advantages its 
introduction into every-day affairs has made but little progress 
and its employment is confined mainly to the sciences. 

7. Unit of Length Selected by Electricians. — The meter is 
subdivided into ten parts, decimeters, a unit but little used, and 
these are again subdivided into ten parts, centimeters. This last 



lllilllll 
1 


lllilllll 

2 


lllilllll 
3 


lllilllll 
4 


lllljllll 



cubic cm. 



centimeter scale 

Fig. 1. 



unit, a length only very little less than four-tenths of an inch, is 
adopted by electricians as their fundamental unit of length. The 
selection of the centimeter rather than the meter was largely in- 
fluenced by the fact that the cubic centimeter of water weighs one 
gram and consequently to determine the specific gravity of a 
solid or liquid substance it is only necessary to obtain the weight 
of a cubic centimeter of it in grams. 

8. The Unit of Mass.— Mass and weight should not be con- 
fused. The mass of a body is the quantity of matter which it 
contains and is invariable but its weight varies as it changes its 
position with respect to the earth's center of gravity. Neverthe- 



4 ELEMENTS OF ELECTRICITY. 

less, the masses of similar bodies under like conditions are propor- 
tional to their weights and practically we compare masses by 
comparing their weights. 

In the metric system the unit of mass is the mass of a cubic 
decimeter of distilled water at its maximum density, 4° C. The 
weight of this, the kilogram (about 2.2 pounds), is the French 
industrial unit of weight and is perpetuated in a platinum standard. 

The kilogram being inconveniently large for their purposes, 
electricians and other physicists have taken as their fundamental 
unit the gram, the mass of a cubic centimeter of distilled water 
at 4° C. Our five-cent nickel coin weighs about 5.26 grams. 

9. The Unit of Time. — The unit of time used by electricians 
is the mean solar second. As the earth's orbit is not circular but 
elliptical, the velocity of the earth varies at various points and 
the apparent solar day, or the interval of time between two suc- 
cessive passages of the sun across the meridian, also varies. The 
average throughout the year of these apparent solar days is taken 
as the mean solar day and this is considered as composed of 24 
hours of 60 minutes of 60 seconds, or as divided into 86,400 mean 
solar seconds. 

10. The C. G. S. System. — The centimeter, the gram and the 
second were recommended as fundamental units by a committee 
of the British Association in 1873 and were formally adopted by 
the International Congress of Electricians in Paris in September, 
1881. From these are obtained the various derived units and the 
system is therefore usually referred to as the "C. G. S. system." 

11. Absolute Units. — Derived units are of two classes, absolute 
and practical. The term absolute, first used in this connection 
by Gauss, is applied to those units which are derived from the 
fundamental units of the system, depend upon them absolutely 
and exclusively and are independent of the force of gravity or of 
any instrument or apparatus or of any arbitrary weight or size 
of any arbitrary material. Many of the absolute units are incon- 
veniently small, others are inconveniently large, and this gives 
rise to the practical units which more nearly fulfill the require- 
ments of the practical electrician. 

Area. — The absolute unit of area is the square centimeter. 
Volume, — The absolute unit of volume is the cubic centimeter. 



INTRODUCTORY. 5 

Velocity. — The absolute unit of velocity is the velocity of a 
body which moves at the rate of one centimeter per second. The 
practical unit in the metric system is one meter per second and in 
the English system one foot per second. 

Acceleration. — Acceleration is the rate of change of velocity and 
the absolute unit is the acceleration of a body which changes its 
velocity one centimeter per second. 

Force. — Force is measured by the acceleration which it imparts 
to a given mass. The absolute unit, the dyne, is that force which 
acting for one second upon a mass of one gram causes its velocity 
to change one centimeter per second. If the mass starts from rest, 
at the end of the first second it will have acquired a velocity of 
one centimeter per second ; if the mass be moving its velocity will 
be accelerated or retarded one centimeter per second. The dyne 
is a very small force. The weight of one gram corresponds to 981 
dynes, that of our five-cent piece to about 5160 and the head of 
the average pin to about 15. The practical unit in the English 
system is the pound, which is nearly 445,000 dynes. 

Work. — Work is the expenditure of energy in overcoming a 
resistance over a path. The absolute unit of work, the erg, is the 
work performed in pushing or pulling against a force of one dyne 
over a path of one centimeter. The erg is a very small unit. The 
English practical unit, the foot-pound, or the work performed in 
lifting a weight of one pound for one foot against the force of 
gravity, is in round numbers 13,560,000 ergs. 

Energy. — Energy is the capacity of a body to do work and 
hence is measured by the work which it can do, therefore, the 
absolute unit of energy is also the erg. 

Heat. — The absolute unit of heat, the small calorie, is the 
amount of heat required to raise the temperature of one gram of 
water from 0° to 1° on the Centigrade scale. According to the 
latest determination of the mechanical equivalent of heat it re- 
quires an expenditure of 1402 foot-pounds to raise one pound of 
water from 0° to 1° C. The small calorie is therefore equivalent 
to 42,000,000 ergs. 

In the C. G. S. system the practical units are some power of 
ten times the absolute units and these practical units have been 
named after distinguished electricians. 



ELEMENTS OF ELECTRICITY. 



CHAPTER 2. 

ELECTRICITY. 

12. Origin of the Name. — Among the stones esteemed pre- 
cious by the ancients was amber to which the Greeks applied the 
name "elektron." This substance, which is now known to be a 
fossil resin, is found in various localities but especially along the 
shores of the Baltic where it is cast up on the beaches after storms. 
It was prized on account of its golden yellow color and luster and 
also because of certain talismanic properties attributed to it. It 
is quite soft and easily fashioned into beads which can be given a 
high polish by rubbing with a dry, woolen cloth. The workmen 
engaged in preparing these soon noticed that upon rubbing a piece 
it acquired a property which it had not before possessed, that is, 
it attracted to itself light substances such as particles of lint and 
dust, bits of straw, feathers, etc. This property quickly died 
away but could be revived by renewed rubbing. These obser- 
vations are recorded by writers of 2500 years ago who, as was 
usual in such cases, fell back upon the supernatural for an explana- 
tion and ascribed to the substance certain mystical qualities. 

For over two thousand years such remained the state of knowl- 
edge. During the reign of Queen Elizabeth a certain Doctor 
Gilbert, an Englishman, carried out a very remarkable series of 
experiments and observations upon the then vaguely known 
properties of magnets, and as allied to magnets investigated other 
bodies in which powers of attraction could be produced. He dis- 
covered that this property was by no means confined to amber 
and in Chapter II, Book Second, of his work, De Magnete, Mag- 
neticisque Corporibus (On the Magnet and Magnetic Bodies), 
published in 1600 he enumerates a list of substances, mainly 
vitreous or crystalline and resinous or resinoid, which possess it. 
He mentions among others the diamond, sapphire, opal, varieties 
of rock crystal, glass, fluor spar, rock salt, mica, sealing wax, resin, 
jet, sulphur, etc., and to all these bodies in which, like amber or 
elektron, the power of attraction could be produced by rubbing 
he applied the term "electrics." From this it was an easy transi- 



INTRODUCTORY. 7 

tion to the word "electricity" applied both to the study or science 
and to the agent itself. 

13. Electricity. — At the very outset we are compelled to admit 
that we do not know what electricity is. It is not matter since it 
is devoid of physical dimensions and weight; yet in its production, 
transmission and manifestation it must always be associated with 
matter. Mechanical or chemical energy applied to matter at one 
point may be used to produce electricity which may be trans- 
mitted to some other point and there used to reproduce energy of 
either kind. Its great value in the industrial world consists in 
this very ability to transfer energy instantly to great distances 
and to deliver it with minimum loss. 

Fortunately for our purposes a theory is not essential, for 
although our knowledge of the agent, electricity, is restricted to 
the various phenomena which it produces, the laws under which 
it operates are definite and well known and under any given set 
of conditions we are able to predict what the electrical outcome 
will be. The study of electricity which we are about to take up is 
therefore but an orderly and logical presentation of these phe- 
nomena and of the laws which govern them. 

14. Divisions of the Subject. — Like any other science elec- 
tricity can not be studied as a whole but must be separated into 
subdivisions, more or less artificial, and these subdivisions taken 
in such order and detail as may appear most suited to the develop- 
ment of the subject while at the same time avoiding undue repeti- 
tion or presentation of facts involving anticipation of principles 
not yet explained. 

It is customary to consider electricity under four heads cor- 
responding to the four conditions under which its effects are 
usually observed. 

1st, Electricity may exist as a motionless charge upon bodies. 
If a wooden ball at the end of a stiff wire be dipped under water 
.and then withdrawn it will be covered with a film of moisture and 
this is very roughly analogous to the charge of electricity which 
may be imparted to a metal ball supported upon a glass stem. 
This is termed stationary or static electricity. 

2nd, With a suitable path to direct it, electricity may flow in a 
constant stream. This is current electricity. 



8 ELEMENTS OF ELECTRICITY. 

3rd, Associated with certain metals, mainly iron, its oxides and 
steel, there are met manifestations, termed magnetic, which take 
the form of forces traversing the metal, emerging at one end, 
following a curved path and re-entering at the other end. An 
electric current is surrounded by similar whirling forces; electricity 
may be made to produce magnetic effects and conversely from 
magnetic forces electricity may be produced. A third division 
is therefore magnetism. 

4th, Finally, typically in the case of wireless telegraphy, the 
electricity is not in the form of a charge nor of a current but by 
means of a very rapidly alternating discharge there are set up 
and transmitted through space intermittent oscillations or waves 
which impinging upon distant conductors, suitably arranged, 
produce in these conductors corresponding oscillating currents. 

Prom a practical standpoint, the least important of the above 
is the static electricity but it is now to be considered because of 
its historical interest, its development being chronologically the 
first and associated with the names of many noted scientists, 
among whom our Franklin played a prominent part. It also 
enables us to present in a simple manner certain useful principles 
and conceptions and thus serves as a stepping-stone to what 
follows. 



STATIC ELECTRICITY. 

PART I. 
STATIC ELECTRICITY. 



CHAPTER 3. 

ELECTRIC ATTRACTION AND REPULSION. 

15. Electric Attraction. — If on a dry day a rod of glass or of 
resin or of some resinoid substance such as amber, sealing wax, 
vulcanized rubber, sulphur, celluloid, etc., be rubbed with a piece 



Fig. 2. 

of fur or woolen cloth (wool is fur) and then held immediately 
above small particles of light substances such as bits of tissue 
paper, feathers, straw or chaff, the particles will leap up and cling 
to the rod. In the case of a glass rod the effect is more pronounced 
if it be rubbed with silk instead of with fur. The rod is said to be 
electrified and the state persists for some time in dry weather but 
disappears quickly if it be damp. The electrification is instantly 
lost if the rod be rubbed over its entire surface with the hand, or 
if it be dipped into water or passed quickly through a flame. 

If an excited or electrified rod be held above a small block of 
wood no appreciable effect will be produced, but if the block be 
cut up into fine shavings they will be readily attracted. Although 
the block is attracted the electric force is too feeble to move it as 
a whole but easily moves the light pieces. In experimenting with 
electric attraction, on account of this feebleness it is customary to 




10 ELEMENTS OF ELECTRICITY. 

use balls of pith, a substance which combines bulk with extreme 
lightness. 

16. Electrified Bodies Attract Non-Electrified. — An electrified 
body attracts all non-electrified, including the metals, liquids, etc. 
Gilbert, who made this discovery, excepted only such bodies as 
are ' 'afire or flaming or the thinnest air" and devised a piece of 
apparatus, a versorium (rotating needle, revolving pointer), by 

which this may be shown. Light 
g ^ — ^n k \j needles of various substances were 

made and like compass needles 
balanced free to turn upon a pivot. 
If these be approached by an electri- 
fied body they will turn towards it. 
If an electrified piece of amber be 
held above a spherical globule of water the globule will assume a 
conical shape as if reaching up to the amber, so also the dense 
smoke from a recently extinguished candle will be attracted. 

17. Electrified Bodies are Attracted by Non-Electrified. — The 

attraction between an electrified body and a non-electrified is 
mutual. This follows necessarily from a fundamental principle 
of mechanics but may easily be shown by suspending by a fine 
thread an electrified rod so as to turn horizontally like Gilbert's 
versorium. If a non-electrified body be held near, the rod will 
be attracted and turn towards it. 

18. Electric Charge. — If two rods of sealing wax be rubbed 
with a woolen cloth they each become electrified. If they be 
rubbed one against the other no effect is produced. Finally, if 
one be electrified by rubbing and then the second be touched by 
the first, the second will be found to be slightly electrified. In 
other words, the electrified rod communicates a portion of its 
electrification to the non-electrified. The electrification upon a 
body is spoken of as a charge; an electrified body is said to be 
charged; and when the electrification is withdrawn it is said to be 
discharged. 

19. Conductors and Non-Conductors. — In 1729 Stephen Gray, 
experimenting with electric attraction, used, instead of a glass 
rod, a tube into the open ends of which he had stuck corks to keep 
out the dust. Upon rubbing the glass tube he was surprised to 
find that the corks which had not been rubbed had nevertheless 



STATIC ELECTRICITY. 



11 



acquired the property of attraction as if the charge generated 
upon the glass had spread upon them. To test this further he 
inserted in the corks long wands of wood or metal terminating in 
balls and found that when the glass was rubbed the balls attracted 
light objects. In place of the wands he next tried cords and wires 
by which he suspended a ball from a glass tube held in a balcony 
above and found that the ball became electrified as soon as the 
tube was rubbed. Wishing to continue this experiment at a 
greater distance than could be obtained from his balcony he was 
obliged to stretch his cord hori- 
zontally, and to keep it clear of 
the ground he hung it up at inter- 
vals by bits of thread attached 
to a line of posts. Under these 
conditions he was unable to elec- 
trify the ball and he surmised 
correctly that the charge had 
escaped by way of the suspending 
threads. A friend who was assist- 
ing him suggested that they use 
a smaller thread which would 
give a smaller path by which the 
charge could escape and a spool 
of silk being at hand it was tried 
with the result that he was able 
to electrify the ball at greater and 
greater distances up to as far as 
765 feet. Finally, the silk thread 
breaking under the strain, he 
tried a fine wire, even smaller than 
the silk, but was unable to elec- 
trify the ball and now perceived 
for the first time that the escape 
of the charge depended not upon 
the size of the suspensions but 
upon the material of which they 
were made. As a result of a con- 
tinuation of these experiments he was enabled to arrange all bodies 
in two classes, one which transmitted electricity to a distance and 
which he called conductors, the other preventing this transmission 







12 ELEMENTS OF ELECTRICITY. 

and called non-conductors or insulators. In the light of modern 
investigation we now know that there is no strict dividing line 
between the two and that there is no such thing as a perfect con- 
ductor nor a perfect insulator but that all bodies offer resistance 
to the passage of electricity, those that offer but little being 
termed conductors, those that offer a great deal being termed 
non-conductors. Joubert concisely defines good conductors as 
those bodies which when electrified at one point are immediately 
found to be electrified all over. 

20. Table of Conductors and Non-Conductors. — In the follow- 
ing list the commoner conductors, partial conductors and non- 
conductors are arranged in order of their conductivity beginning 
with silver, the best conductor, and ending with air, the poorest 
conductor (or best non-conductor). This arrangement is not 
rigorously exact since relative conductivity may vary with change 
of temperature and other circumstances: 



Good Conductors: 


Non-Conductors: 


Silver 


Slate 


Copper 


Oils 


Aluminum 


Porcelain 


Brass 


Leather 


Platinum 


Paper 


Iron 


Wool 


Lead 


Silk 


Mercury 


Resin 


Fair Conductors: 


Rubber 


Compact carbon 


Shellac 


Acid solutions 


Vulcanized rubber 


Salt solutions 


Mica 


Living plants 


Paramne 


Damp earth 


Glass 


Partial Conductors: 


Air 


Water 




Animal bodies 




Flame 




Cotton 




Woods 




Marble 





The foregoing explains why an electrified body is discharged 
when rubbed with the hand or dipped into water or passed through 
a flame, also why, as Gilbert discovered, damp weather is unfavor- 
able for the production of electrification. 



STATIC ELECTRICITY. 



13 



21. All Bodies Susceptible of Electrification. — In contradis- 
tinction to his electrics Gilbert designated as non-electrics those 
bodies in which he was unable to produce electrical attraction by 
friction. Among these he enumerates various flints and agates, 
marble, bone, ivory, the metals, the lodestone, the human body, 
etc. We now know that he was in error in supposing that they 
could not be electrified. Examination of the table above will 
show that his electrics are all non-conductors and his non-electrics 
are all conductors. When he attempted to electrify a piece of 
metal the charge upon it was instantly conducted away. If the 
metal be attached to a glass handle it is readily electrified. If a 
person stand upon a glass-legged stool or upon a cake of resin or 
be suspended by silk cords and then be touched by an electrified 
glass rod or stroked by a piece of fur he will be strongly electrified, 
small light particles will fly to him as to the electrified amber and 
if a second person attempt to touch him, just when the distance 
between the outstretched hand and the electrified person becomes 
very small a faint snapping noise will be heard and both persons 
will perceive a slight pricking sensation. In the dark it will be 
seen that this noise accompanies a spark. All bodies if properly 
insulated so that the charge upon them can not escape may be 
electrified. 

22. Electric Repulsion. — Reverting to the first experiment in 
electric attraction (Par. 15), if 
the electrified rod with the par- 
ticles adhering to it be observed 
for a brief interval, the par- 
ticles will be seen to leap or 
dart away from the rod as if 
shot away by a repelling force. 
This repulsion does not take 
place until after the particles 
have been in contact with the 
electrified rod. To exhibit this 
better, use is made of the so- 
called electric pendulum, a pith 
ball suspended by a fine silk 
thread (Fig. 5). If the ball be 
approached by an electrified rod 
it will fly to the rod and after a short contact will be repelled. 






Fig. 5. 



14 ELEMENTS OF ELECTRICITY. 

If the rod be moved in pursuit the ball will continue to move 
away avoiding the rod. The ball is now charged, as may be 
shown by its being attracted by any non-electrified body held 
near it; the repulsion must therefore be due to the charge which it 
acquired by its contact with the rod. 

23. Two Kinds of Electrification. — If the pith ball of an electric 
pendulum be approached by a stick of sealing wax which has been 
rubbed with fur, it will first be attracted and after contact will be 
repelled. Similarly, if it be approached by a glass rod which has 
been rubbed with silk, it will be attracted until contact is made and 
thereafter repelled. But the strange part is that the ball repelled 
by the electrified sealing wax is attracted by the electrified glass 
and the ball repelled by the glass is attracted by the sealing wax. 
The electrification produced upon the glass must therefore be dif- 
ferent from that produced upon the sealing wax. Dufay, who in 
1733 made this discovery, designated these by the terms vitreous 
and resinous, vitreous being that produced by rubbing glass 
with silk and resinous that by rubbing sealing wax with fur. It 
has since been discovered that the kind of electricity produced 
does not depend entirely upon the material of the body rubbed 
but also upon that of the rubber and moreover varies in a sur- 
prising manner with the polish, the temperature and even the 
color of the body rubbed. Glass rubbed by silk is vitreously 
electrified but if it be rubbed by fur it is resinously electrified. 
It is possible to arrange a list of substances so that any one 
body in it is vitreously electrified when rubbed by any other 
below it on the list. The following is such a list: — Fur, glass, 
flannel, feathers, silk, paper, wax, metals, vulcanized rubber, 
celluloid. 

In view of the above it is better, for reasons given in Par. 27, to 
follow Franklin and employ the terms positive and negative, L ". Q 
vitreous being positive, the resinous negative. 

24. Like Charges Repel, Unlike Attract. — If two pith balls sus- 
pended side by side by separate silk threads (Fig. 6) be approached 
by an electrified rod of glass or of sealing wax they will both be 
attracted to the rod and, as soon as they have touched it, will be 
repelled, but not only this, they will repel each other and no 
longer hang side by side but will diverge and stand apart. If two 
separate pendulums be used and the pith ball of one be charged 




STATIC ELECTRICITY. 15 

from a glass rod, the other from a rod of sealing wax, the balls 
will attract each other. We therefore see 
that bodies charged with like electricity repel 
each other; those charged with unlike elec- 
tricity attract each other. 

25. Electroscopes. — Instruments for deter- 
mining (a) whether a body is charged or not 
and (b) the nature of the charge are called 
electroscopes. The simplest form of an elec- 
troscope is Gilbert's versorium described in 
Par. 16. The electric pendulum is frequently 
used as an electroscope. If the pith ball after 
being touched by the hand is attracted by 

the body being investigated, the body is charged. After we have 
in this way ascertained that the body is charged we next deter- 
mine the nature of the charge by charging the pith ball, say posi- 
tively, or from a glass rod which has been rubbed by silk, after 
which when held near the body it will be repelled if the latter be 
charged positively and attracted if it be charged negatively. 

26. Simultaneous Production of Equal Amounts of Both Kinds 
of Electricity. — In producing electricity by friction the body 
rubbed acquires a certain kind of charge and the rubber acquires 
the other kind; thus in rubbing a glass rod with silk the rod is 
charged with vitreous or positive electricity and the silk can be 
shown to have a resinous or negative charge. Furthermore, as 
may be shown in several ways, the amounts of the two kinds are 
exactly equal. If two substances are rubbed together and acquire 
opposite charges and their charges be imparted successively to a 
third body the third body will not be electrified. If a disc of glass 
ai jiie covered with silk, both being mounted on glass handles,be 
ruubed together they will each separately attract pith balls but 
when placed together will have no effect, the charge on the one 
exactly counterbalancing or neutralizing that on the other. 



27. Theories of Electricity.— Two theories were advanced to 
account for the above phenomena. The first is Symmer's Two 
Fluid Theory. According to this there exist in all bodies two 
electrical fluids of opposite kinds but in exact balance, thus neut ra- 
izing each other. When a body is excited by friction this balance 



16 ELEMENTS OF ELECTRICITY. 

is disturbed and one of the fluids is drawn off upon the rubber 
leaving the remaining fluid unbalanced and in excess. In this 
country the theory most generally held was Franklin's Single 
Fluid Theory which is to the effect that all bodies in their natural 
state are charged with a certain quantity of electricity, in each 
body this quantity being of definite amount. When two bodies 
are rubbed together, one parts with a portion of its electricity 
which is appropriated by the other. The latter then has more 
than its normal share and is positively electrified; the former has 
less and is negatively electrified. 

The theory at present accepted is the Electron Theory. We 
are taught in Chemistry that, according to the atomic theory, all 
matter is composed ultimately of small, indivisible particles 
called atoms, the atoms of any one element being all of the same 
weight, which is different from that of the atoms of any' other 
element. These atoms are now thought to be rather complex 
bodies arranged somewhat after the manner of a solar system and 
consisting of a core or nucleus carrying a positive charge of elec- 
tricity and surrounded by a greater of less number of very minute 
bodies, electrons, which carry negative charges. From whatever 
element the electrons be derived, they are supposed to be the 
same, and they all carry equal charges. These charges being 
the smallest obtainable quantity of electricity, electricity is seen 
to be atomic in character (Par. 280). The mass of an electron 
is about 1800 times smaller than that of an hydrogen atom. 
Under normal conditions, the aggregate of the negative charges 
of the electrons of an atom is equal to the positive charge of the 
nucleus, and the resultant electrification is zero. It is, however, 
possible in a number of ways to displace one or more electrons 
from the atom. The electron carries away with it a negative 
charge leaving the atom charged relatively positively. If, there- 
fore, a body be charged positively, it has lost some of its electrons; 
if it be charged negatively, it has an excess of electrons. This 
theory will be developed as we proceed. 

It is proper to state here that although we do not know what 
electricity is, we do know that it is not a fluid, yet we retain the 
term for convenience. Finally, no satisfactory explanation is 
given why bodies should acquire unlike charges by friction. The 
amount of electrification is not proportional to the amount of 
mechanical energy spent in friction. 



STATIC ELECTRICITY. 



17 



CHAPTER 4. 



ELECTROSTATIC INDUCTION. 

28. Electrification by Influence. — In Fig. 7, A represents a 
metallic ball attached to a stand by a glass stem and B a metallic 
cylinder similarly mounted and carrying on its under side a series 
of pairs of pith balls hanging from linen threads. So far as elec- 
trical results are concerned, it is immaterial whether the ball 
and cylinder be solid or hollow. They may even be of wood 
covered with tin-foil or gilded but are usually made of thin brass. 




c 



(£l 



7V^ J~H 
B 



7\ 



) 



Fig. 7. 

If now the ball A, while at some distance from B, be given a charge, 
say positive, and then be moved up towards B, the pith balls 
beneath B will be observed to diverge indicating that B is charged. 
Since A has not touched B and since the same effect is produced 
when a sheet of glass is interposed between A and B and, finally, 
since it can be shown that the charge upon A is undiminished, the 
charge upon B could not have been communicated from A but 
must have been induced or produced by the influence of A's charge. 
This phenomenon may be called "induction" but, as will be seen 
later, there is a more important and different kind of induction 
and it is better to use the term "influence." If A be withdrawn, 
the charge upon B disappears. 

29. Distribution of the Induced Charge. — If we return to the 
preceding experiment and examine B while it is under the in- 



18 ELEMENTS OF ELECTRICITY. 

fluence of A, it will be noticed that the pairs of pith balls do not 
diverge to the same extent, those at the ends standing far apart 
but the divergence decreasing towards the center and the pair at 
the center not diverging at all. This indicates that the charge 
has accumulated at the ends of B and that the center is not charged. 
Examination with an electroscope will show that the charges at 
the ends of B are of different kinds, that nearest A (in the case 
assumed) being negative, that farthest away being positive; in 
other words, the positive charge on A has induced on B and drawn 
as near to itself as possible a negative charge and repelled as far 
as possible a positive charge. 

In Par. 24 it is stated that bodies charged with like electricity 
repel each other and those charged with unlike attract. The 
above experiment seems to indicate that it is not the charged 
bodies that attract or repel each other but the charges them- 
selves. A fuller explanation of the phenomenon of induction 
is given later on (Par. 75). 

30. Electric Attraction and Repulsion Explained. — The fore- 
going affords an explanation of the phenomena of attraction and 
repulsion already described. When an electrified rod is presented 
to a pith ball, a like charge is induced on the far side of the ball 
and an opposite charge on the near side. The like charge is 
repelled, the opposite attracted and the opposite being the nearer, 
the force of attraction is greater than that of repulsion and the 
ball moves bodily to the rod. Upon contact with the rod 
the opposite charge on the ball is neutralized by a portion of 
the charge on the rod, leaving the ball with the same kind of 
charge as that remaining on the rod and consequently the ball is 
repelled. 

31. Amount of Induced Charge. — A given charge always in- 
duces on surrounding objects an exactly equal opposite charge. 
If a small charged sphere be placed at the center of a hollow con- 
ducting sphere there will be induced upon the inner surface of the 
latter an exactly equal opposite charge, and this no matter 
what the size of the outer sphere or the thickness or the nature 
of the intervening non-conductor. If the charged sphere be dis- 
placed from the center so as to be nearer one side of the cavity 
than the other, the amount of the induced charge is unaltered 



STATIC ELECTRICITY. 19 

but the greater portion will accumulate upon the side of the 
cavity nearest the sphere. A charged body inside of a room 
induces upon the ceiling, walls, floor and surrounding objects 
opposite charges which in the aggregate exactly equal the central 
charge and which accumulate most upon those objects nearest 
to it. Finally, if the charged body be at a distance from others, 
as for example in an open field, the induced charge will still be the 
same but will be spread over the surface of the ground, the greater 
portion being immediately beneath the body. If while in this 
position a conducting body be brought up close to it, practically 
the entire induced charge will be found upon the second body and 
the portion upon the earth becomes so small that it may be 
neglected. In ordinary laboratory experiments where the charged 
body is a foot or more from the table beneath and is supported 
by an insulated stem and the conductor upon which the charge is 
induced is brought up to a distance of an inch or so from the first, 
the induced charge upon the table and more distant objects 
becomes less and less and gathers more and more upon the con- 
ductor. Under such conditions we may say that the amount of 
the induced charge upon the conductor depends upon — 

(a) The amount of the primary or inducing charge; 

(b) The distance between the primary and the induced charge; 

(c) The nature of the medium between them. 

The greater the primary charge, the greater its influence and the 
greater the induced charge. 

The nearer the primary charge to the conductor, the greater 
the induced charge. 

With a constant primary charge at a constant distance from the 
conductor, the amount of the induced charge is found to vary with 
the nature of the separating medium, that is, whether it be air or 
oil or glass or sulphur or mica or other non-conductor and this 
variation is not in proportion to the value of the substance as a 
non-conductor but to an inherent property of the substance 
termed by Faraday its dielectric capacity (see Par. 90). 

The maximum charge that could ever be induced is one at the 
far end of the conductor equal and similar to the primary charge 
and one at the near end equal and opposite. As the distance 
between the primary and the opposite induced charge diminishes 
a point is reached where the attraction between them becomes 



20 



ELEMENTS OF ELECTRICITY. 



great enough to break down the resistance of the remaining 
thickness of the medium intervening, a spark leaps across, the 
primary charge and the opposite induced charge neutralize each 
other, the original charged body is found to be discharged and 
the conductor is left charged with the similar charge which at 
first was repelled to its far end. 

32. Separation of the Induced Charges. — If we repeat the pre- 
ceding experiment with the charged ball A and a divided con- 




c 



B 



XJ 



X7 



3 



fttE m fl 



Fig. 8. 

ductor consisting of two parts B and C, Fig. 8, which may be 
placed in close contact, the induced positive charge will be repelled 
Into the far end C and the negative charge drawn into the near 
end B. While under the influence of A, C may be removed first 
and then B and each will be found to be charged, C positively and 
B negatively. If the two parts while distant from A be again 

joined together their electrifica- 
tion vanishes. This is an addi- 
tional proof of the fact stated 
in Par. 26 of the simultaneous 
production of equal amounts of 
both kinds of electricity. 

33. Free and Bound Charges. 

— Let us again consider the case 
of the charged insulated ball and 
the insulated conductor as shown 
in Fig. 9. The positive charge on 




c 



B 



} 



Fig. 9. 



A has induced and attracted to the near end of B a negative 
charge which is held securely by their mutual attraction. The 
hand may be placed on B, sl wire may be attached to the near 



STATIC ELECTRICITY. 21 

end of B, still the negative charge refuses to budge and the only 
way by which it can be made to shift its position is by connect- 
ing it to some conductor which will allow it to approach A nearer 
than it is now. Such a charge, that is an induced charge held by 
a primary charge of the opposite kind, is said to be "bound." 
On the other hand, the positive charge on the far end of B is 
being repelled by A and will take advantage of any path what- 
soever which will enable it to withdraw more remote from A. 
Thus if the hand be placed upon the near end or upon any other 
point of B the positive charge immediately escapes through the 
body and finally to the earth, even though in doing so it must 
in a part of its pathway draw nearer to A. Such a charge, in 
contradistinction to the bound charge, is said to be "free" and 
this name is also applied to any charge upon an insulated con- 
ductor not under the influence of some other charge. Since the 
free charge always escapes when the conductor is touched and the 
bound charge remains, the following rule is given : If while under 
the influence of a charged body a conductor be touched, it acquires a 
charge of the opposite sign. 

We are now in a position to understand the operation of 
two pieces of apparatus, the gold-leaf electroscope and the 
electrophorus. 

34. The Gold -Leaf Electroscope.— This is a very sensitive piece 
of apparatus for detecting the presence of electric charges and 
determining their character. The simplest form consists of a 
glass jar (Fig. 10) closed by a stopper of insulating material 
through which passes a brass rod which terminates above in a 
metal knob or disc and below is bent like the letter L. Fastened to 
the horizontal arm of the L so as to hang face to face in contact 
and vertically are two small ribbon-like strips of gold-leaf. This 
is used because on account of its extreme thinness it is lighter than 
any other material of equal strength and adds the advantage of 
being an excellent conductor. The glass jar serves as an insulating 
support and protects the leaves from currents of air which would 
cause them to flutter. When a charged body, such as an electri- 
fied rod of glass or of sealing wax, even though the charge be very 
small, is brought within a foot or so of the apparatus the hanging 
leaves will diverge. The explanation is that the charged body 
induces and attracts an unlike charge into the knob of the appara- 
tus and repels a charge of similar kind to its own as far as possible, 



22 



ELEMENTS OF ELECTRICITY 



that is, into the gold leaves; these having like charges repel each 
other and stand apart. 

To determine the nature of a charge, the electroscope is given a 
preliminary charge of a known kind. This causes the leaves to 




Fig. 10. 



diverge. If now it be approached by a charge of the same kind 
the leaves will diverge more while if the charge be of opposite 
kind they will droop together. 

By taking advantage of the principle given in the preceding 
paragraph we may with a single charged body impart to the 
electroscope a charge of either kind desired. Thus with a posi- 
tively charged glass rod we may touch the knob and impart a 
slight positive charge (we really neutralize the induced negative 
charge in the knob and leave the induced positive charge). To 
charge it negatively we hold the glass rod near the knob (Fig. 10) . 
This induces a bound negative charge and a free positive charge. 
If now the knob be touched by the remaining hand the free charge 
will be removed as will be indicated by the leaves instantly falling 
together. Now withdraw the hand and finally remove the rod. 
The bound negative charge, which had been attracted into the 
knob, will surge back and distribute itself as will be shown by the 
leaves again diverging. 



STATIC ELECTRICITY 



23 




Fig. 11. 



35. The Electrophorus. — Volta's invention, the electrophorus, 
Fig. 11, an instrument for producing static charges by influence, 
consists of two parts. The first, 
analogous to the charged rod used in 
the experiments described in the pre- 
ceding paragraph, is a flat cake of 
some resinoid body, resin, sealing 
wax, sulphur, vulcanized rubber or 
celluloid, mounted in a shallow 
metal dish. The second is a circu- 
lar disc of metal, or of wood covered 
with tin -foil, at the back of which is a 
glass handle. To use the instrument, 
the cake dry and free from dust is 
rubbed with a warm, dry, woolen 
cloth or piece of fur. It thus acquires a negative charge. The 
metal disc is then placed upon the cake. It is in mathematical 
contact with the cake in only a few points and the cake being a 
non-conductor only the minute portions of the charge at these 
points of contact flow into the disc. Therefore the disc is a con- 
ductor separated from a charged body, the cake, by a layer of air 
as thin as a sheet of paper and consequently a bound positive 
charge is induced upon its lower face and a free negative charge 
upon its upper face. While in this condition it is touched by the 
finger, the free charge escapes and, in accordance with the rule in 
Par. 33, it is left with a positive charge. It may then be lifted by 
the glass handle and its charge being no longer bound can be used 
to give a spark, to charge other bodies, etc. As practically none of 
the primary charge on the cake is removed, this process could be 
repeated an indefinite number of times without the necessity of 
recharging the cake but, as a matter of fact, the primary charge 
gradually weakens due to leakage into the air. 

In the production of electricity, energy must always be expended. 
It requires more force to pull the disc away from the charged cake 
than it does from the cake before it is charged; the extra energy 
thus expended accounts for the production of the charge. 

Machines have been invented by which this operation of bring- 
ing up the conductor, touching it and then withdrawing it is per- 
formed automatically and the movement of these machines, being 
one of rotation, the production of the charge is almost continuous. 



24 ELEMENTS OF ELECTRICITY. 



CHAPTER 5. 
DISTRIBUTION OF CHARGE. 

36. Charge on a Non- Conductor. — An electric charge imparted 
to a body is differently distributed according to whether the body 
is a conductor or a non-conductor. In the case of a non-conductor 
the charge clings to the spot where it was generated or placed. If 
a stick of sealing wax be rubbed, only the part which has been 
rubbed will be found to be charged. If a cake of non-conducting 
material be touched by a charged body, only the spots actually 
touched will be charged. If such a cake be charged over its entire 
surface and then be touched by the finger or by a conductor, only 
the spots actually touched will be discharged. Lichtenberg 
devised a means by which the above may be shown to the eye. A 
charged body is moved like a pencil over a dry sheet of glass or of 
resin and a pattern is traced. Finely powdered red lead and 
sulphur mixed together are then sifted over this pattern through 
a piece of muslin. In the mixing and sifting the red lead becomes 
positively electrified, the sulphur negatively, and if the original 
charge be positive, the sulphur will be attracted, the red lead 
repelled and there will be produced a yellow pattern on a red 
back ground. In performing this experiment it will be noticed 
that the sulphur does not follow absolutely the mathematical 
lines originally traced but spreads slightly in mossy or frost-like 
patterns. Charges while not flowing over a non-conductor still 
have a tendency to creep or spread and the fern-like forms are due 
to minute particles of dust which lead the charge now in one 
direction, now in another. 

37. Charge on a Conductor. — On the other hand, a charge 
imparted to any point of a conductor spreads immediately over 
the entire body and if a charged conductor be touched at any point 
so as to afford a path to the earth it is immediately discharged. 
It is possible with the apparatus described in the next paragraph 
to remove a portion of the charge. As soon as this portion is 
removed the remaining charge redistributes itself. 




STATIC ELECTRICITY. 25 

38. The Charge Confined to the Surface. — With size, shape and 
other conditions constant it is found that the same charge may be 
imparted to a conductor whether it be solid 
or hollow or even made of non-conducting 
material covered with tin-foil or gilded. The 
inevitable conclusion is that the charge 
resides upon the surface of a conductor. This 
is shown directly by the following experi- 
ments. A hollow metallic sphere (Fig. 12) 
with an opening in its top and mounted upon 
a glass support is given a charge. In order to 
take a sample portion of a charge for in- 
vestigation, Coulomb devised a piece of ap- 
paratus which he called a proof plane. This 
is a little circular disc of metal or gilded paper 

fastened to the end of a small glass rod. If the disc be touched to 
a charged body it receives a portion of the charge and may then 
be removed, and the charge tested by an electroscope or otherwise. 
If the charged sphere be touched by a proof plane it will part with 
a portion of its charge. If, however, the proof plane be inserted 
through the opening in the sphere and the inside of the sphere be 
touched, the plane will show no sign of any charge. 

The above fact may be even more conclusively shown as follows : 
A small metal ball suspended by a silk thread is brought into con- 
tact with the outside of the charged hollow sphere. While touch- 
ing the sphere it is practically a portion of the latter's outer sur- 
face and it receives a charge. The charged ball is then lowered 
through the opening until it touches the inside of the sphere. 
At that instant when it forms a part of the latter's inner sur- 
face it is discharged, the charge passing through to the outside of 
the sphere. 

Faraday showed the same thing with a cylinder of wire gauze 
instead of the sphere. 

39. Biot's Experiment. — Another demonstration of the surface 
distribution of the charge is given by Biot's experiment. In Fig. 
13, A is an insulated metallic sphere and B and C are glass-handled 
metallic hemispheres slightly larger than the sphere. If the sphere 
be charged and then the hemispheres placed so as to completely 
cover it but not to touch it the charge will still remain on the sphere. 
If the covers be allowed to touch the sphere the charge will im- 



26 



ELEMENTS OF ELECTRICITY. 



mediately pass to the hemispheres which when separated will be 
found to be charged and the sphere discharged. The reason for 
this is given later (Par. 68). 




Fig. 13. 

As an exception to the foregoing general statement there is one 
set of conditions under which it is possible to have a charge on the 
interior of a conductor. If through the opening of the sphere 
shown in Fig. 12 there be inserted a charged insulated body, there 
will be induced upon the inside of the surrounding sphere a charge 
of opposite kind, the charge of like kind being repelled to the 
exterior. 

Finally, it must be remembered that we are now discussing 
static charges, for, as will be shown later, current electricity 
penetrates throughout the conductor. 

40. Distribution of Charge. — Although, as was stated in Par. 
37 above, a charge imparted to a conductor spreads over it im- 
mediately, the distribution is not uniform but more of the charge 



O 



EHE 



i 1 1 m i ni 



C 



J 



a b c 

Fig. 14. 

will be found about the edges and angles than upon the flatter 
surfaces. In fact, there is only one body, the sphere, upon which 
the distribution is uniform and this is so only when the sphere is 
so remote from other charged bodies that the effects of induction 



STATIC ELECTRICITY. 27 

are not felt. This uniform distribution may be represented 
graphically as in (a) in Fig. 14 by drawing about the circle repre- 
senting the sphere a concentric dotted circle as if the charge were 
a material of the thickness represented by the distance between 
the full and the dotted circles. 

On a metallic disc (b) the charge is heaped up around the edges 
but uniformly distributed over the flat surfaces. Advantage is 
taken of this in a piece of apparatus, the attracted disc electrom- 
eter (Par. 101). 

If the conductor be a cylinder with rounded ends (c), such as 
is used with many electrical machines, the amount of charge at 
the ends is much greater than upon the cylindrical portion. 

41. Surface Density. — -This material conception of the charge 
is not confined to graphic representation but in our calculations 
we may and do treat it as if it were a substance the component 
particles of which repel each other and combine in a resultant 
action upon other charges. Thus we speak of it as spread with a 
certain density over the surface of a conductor or as being denser 
at certain points than at others. This surface density is meas- 
ured by the amount of electrification or number of units of elec- 
tricity per unit area. What these units are is explained later (Par. 
56). An isolated sphere is the only body over which the dis- 
tribution is uniform and the surface density is determined by 
dividing the total charge by the area of the sphere. 

On neither conductors nor on non-conductors may a charge be 
accumulated indefinitely, but when in air the surface density at 
any point reaches about 20 units per square centimeter a discharge 
will occur either along the surface of the body or through the body 
or through the surrounding medium. 

42. Effect of Points.— Coulomb found that in an ellipsoid of 
revolution the surface density at the extremities of the axes were 
to each other as the lengths of the respective axes. In a spindle- 
shaped ellipsoid where the axis of revolution is much longer than 
the minor axis the density at the pointed end is very much greater 
than that on the equatorial surface, and this disproportion in- 
creases as the ellipsoid becomes more and more pointed until 
finally the particles of air adjacent to the point become charged. 
Having like charges, these particles repel each other and are 
repelled from the point. They therefore move off, giving way for 



28 



ELEMENTS OF ELECTRICITY. 



others which likewise become charged and move off, thus produc- 
ing a continuous electric wind and rapidly discharging the body. 
In consequence of the foregoing, all points, sharp corners and 
angles, unless they be designedly used, are carefully avoided in 
electrical apparatus. 

43. Franklin's Experiment. — To illustrate the effect of points 
Franklin devised the following experiment. From the ceiling 
there is suspended by a silk thread a pith ball as large as a marble 
and upon the floor immediately beneath is placed a glass jar upon 
whose mouth is balanced a metal ball (Fig. 15). The thread is of 



-6--. 





Fig. 15. 

such length that the pith ball hangs against the side of the metal 
ball. A charge is communicated to the metal ball and the pith 
ball is at once repelled and hangs at a distance of four or five 
inches. If now a sharp-pointed wire or a needle held in the hand 
be brought up to within six or eight inches of the metal ball, its 
charge is instantly lost as will be shown by the pith ball falling 
against it at once. In the dark a faint light, like that of a firefly, 
will be seen around the point of the needle. Franklin stated that 
the needle drew the electric fire from the ball. A more accurate 
explanation is that the charge upon the ball induced up through 
the body of the experimenter and out to the needle an opposite 
charge which escaped from the point, passed over to the ball and 
neutralized its charge. This experiment is noteworthy as it 
suggested to Franklin the invention of the lightning-rod. 

44. Other Experiments with Points. — The existence of the 
electric wind referred to above can be shown in several ways. If 



STATIC ELECTRICITY. 



29 




Fig. 16. 



a point attached to a charged conductor be held near the face the 
wind can be distinctly felt. If such a point be held close to the 
flame of a candle the flame will be blown to one side or perhaps 
even extinguished. 

As the charged particles of air are repelled from the point, the 
point must experience an equal 
repulsion in the opposite direction. 
This is illustrated by the electric 
whirl shown in Fig. 16. It consists 
of a light metal hub with a set of 
pointed wire spokes, the ends all 
being bent at right angles and all 
pointing in the same direction, 
clockwise or counter-clockwise. 
The hub is placed upon a pointed 
pivot so as to turn freely like a com- 
pass needle. The pivot is connected to an electric machine and 
when a continuous charge is supplied the whirl rotates in the 
opposite direction to that in which the ends of the wires point. 

There is a final point in connection with this electric wind which 
is to be noted. Just as the spray from an atomizer moistens the 
surface against which it is directed, so the electrified particles of 
air striking the surface of a non-conductor impart a charge to this 
surface. This property is utilized in the operation of certain 
electric machines described in the next chapter. 

45. Division of Charge. — If a charged body be brought into 
contact with one not charged, both being insulated, the charge is 
divided between the two in proportion to their electric capacities, 
a property to be defined later (Par. 79). If both bodies be charged 
they may be considered to make common stock of their charges 
and to redistribute the total as stated above. This is true as well 
for charges of opposite kinds; enough of the greater charge is 
consumed to neutralize the lesser and the remainder, whether 
positive or negative, is distributed between the two bodies. 
Spheres of equal size have equal capacities, therefore, if an in- 
sulated charged sphere be touched by an equal uncharged one, 
likewise insulated, the original charge will be divided into halves. 
This enables us to get two similar and equal charges and, as will 
shortly be shown, is of very great importance in the determina- 
tion of the laws of electrical attraction and of repulsion and in 
the measurement of electrical charges. 



30 



ELEMENTS OF ELECTRICITY. 



CHAPTER 6. 



ELECTRICAL MACHINES. 



46. Kinds of Machines. — In the preceding chapters we have 
seen how electric charges may be produced first by friction of dis- 
similar substances and second by influence, as typically in the 
case of the electrophorus. Based upon these two principles there 
have been constructed two distinct classes of machines designated 
respectively as frictional and influence machines. These substi- 
tute for the intermittent motion of friction and for the alternate 
lowering and raising of the disc of the electrophorus a motion of 
rotation by which wasteful expenditure of energy is avoided, the 
production of the charge becomes continuous, and a much greater 
charge can be obtained than by the other means. Many kinds 
have been constructed and though they are of interest the limits 
of time and space restrict us to a brief description and explanation 
of a typical form of each. 

47. Frictional Machines. — Frictional machines comprise three 
parts, the material which is rubbed, the rubber and the body, 
called the prime conductor, upon which the charge is accumulated. 




Fig. 17. 

The earliest form, invented by Von Guericke, consisted of a globe 
of sulphur cast upon a wooden axis by which it was rotated. As 
the globe revolved it was pressed by the bare hand and the charge 
was gathered by a light chain which dangled against the globe 



STATIC ELECTRICITY. 31 

and hung from the prime conductor, an iron bar suspended by 
silk chords. Many changes and improvements were made by 
subsequent inventors. The operation of the modern machine is 
best explained from the form shown in Fig. 17, the cylinder 
machine. 

48. Cylinder Machine. — This consists of a glass cylinder A 
rotating on a horizontal axis, a hair-stuffed pad B pressing 
against one side of the cylinder and the prime conductor C placed 
on the other side and insulated upon a glass support. This con- 
ductor is of hollow brass, of the shape shown, from one end of 
which projects a T-shaped rod carrying on its outer side a row of 
needle-like spikes. The quantity of electricity produced depends 
upon the extent of the two surfaces in contact and also upon the 
material of which these consist. The farther these are apart in 
the list of substances in Par. 23, the greater the electrical effect 
produced by rubbing them together. The material of the cylinder, 
glass, being near the top of the list, the rubber should be some 
substance near the bottom. The metals come near the bottom 
but their rigidity interferes with their use as rubbers. However, 
certain metals dissolve readily in mercury producing a more or 
less pasty amalgam which alone or mixed with grease may be 
smeared upon the rubber. Zinc, tin and the sulphide of tin are 
used in these amalgams. 

The operation of the machine is as follows: The cylinder is 
rotated in a clockwise direction, the glass becomes positively 
electrified, the rubber negatively. As the positive charge on the 
surface of the glass comes around opposite the prime conductor, 
the points are said to collect it or take it off, but actually a nega- 
tive charge is induced on the near end of this conductor, a positive 
charge on the far end, the negative charge escapes from the needle 
points in an electric wind, strikes against the cylinder and neutral- 
izes the positive charge on its surface (Par. 43) and the conductor 
acquires an increasing positive charge. 

If the rubber is insulated, a negative charge may be drawn from 
it but it is generally connected to the ground by means of a light 
chain or otherwise. 

More modern forms use rotating glass plates instead of the 
cylinder but the principle of their operation is the same. It 
will be noted that although designated frictional machines, in- 
fluence as well as friction is involved in the production of the 



32 



ELEMENTS OF ELECTRICITY. 



charge. They are very sensitive to hygroscopic moisture and 
frequently fail to work on account of atmospheric conditions, 
for which reason they are now superseded by the influence 
machines. 

49. Toepler's Influence Machine. — This machine, as shown in 
its simplest form in Fig. 18, consists of two plates of glass mounted 




Fig. 18. 



a short distance apart upon a common horizontal axis about which 
one may be rotated, the other one being fastened rigidly to the 
frame of the apparatus. The rotating plate is circular in form. 
Fig. 19 (in which for clearness the relative proportions and posi- 
tions of the parts have been greatly distorted) represents an 
edgewise view of the glass plates, the eye of the observer being 
supposed to travel around the circumference while being con- 
tinually directed towards the axis of the machine. The letters on 
these two figures correspond. A represents the fixed plate and B 
the moving one, the direction of motion being indicated by the 
arrow. On the outer surface of A and diametrically opposite to 
each other are the two field plates C and D. These are sheets 
of tin-foil glued to the glass, their thickness being greatly exagger- 
ated in Fig. 19. Extending from each of these field plates there is 
a conductor which passes around the outer edge of the two glass 
plates to the appropriating brushes E and F on the outer side 



STATIC ELECTRICITY. 



33 



of the revolving plate. These brushes are of fine brass wire 
like a paint brush and sweep along the face of the plate B as 
it revolves. On the outer surface of B there are glued six 
carriers, G, H, J, K, L, M, 
likewise of tin-foil. Outside 
of these and opposite the 
farther edge of the field plates 
are the neutralizing brushes, 
N and P, connected to each 
other by a conductor. Mid- 
way between the appropriating 
and the neutralizing brushes 
are the two combs, Q and R, 
which connect to the two dis- 
charging knobs, S and T. These 
knobs are on the ends of rods 
which by means of the glass 
handles U and W may be slid 
in or out thus adjusting the 
distance between the knobs. 
The operation of the machine 
is as follows: From an excited 
glass rod Z a small initial 
charge is imparted to the plate 
C. This induces a negative 
charge on the inner side of the 
carrier H and a positive charge 
on the outer side. As the plate 
B rotates H moves to the po- 
sition J where it is touched 
by the neutralizing brush N 
which allows its free positive 
charge to escape, as shown by the small arrow, and leaves it with 
a negative charge. Upon reaching the position K the greater 
part of this negative charge, being no longer bound, is drawn off 
by the appropriating brush F and conveyed to the field plate D. 
When the carrier reaches the position L the negative charge on D 
induces a positive charge on the inner surface and a negative 
charge on the outer. In the position M the carrier is touched by 
the neutralizing brush P and the free negative charge is neutral- 




34 



ELEMENTS OF ELECTRICITY. 



ized by the positive charge coming from N, M being left with a 
positive charge. The carrier next reaches G, is touched by the 
appropriating brush E and gives up the greater part of its charge 
to the field plate C. C now has a greater positive charge than in 
the beginning and its inductive action upon H is greater. In this 
manner as the carriers rotate they add to the charges on the field 
plates. This does not continue indefinitely. The field plate C 
being much larger than the carrier G has a much greater capacity. 
This property is defined later but for the present we may say (in 
a figurative sense) that C requires more electricity to fill it up 
than does G but once that it is filled up no more will flow into it 
from G. However, induction continues to act and the unappro- 
priated charges on the carriers are now taken off by the combs 
Q and R as was explained in the description of the frictional 
machine, and it is this surplus electricity which we draw from the 
machine. In this machine, as in the frictional machine, it will be 
noted that two kinds of electricity are involved in the production 
of the charge, the initial charge being produced by frictional 
electricity. 

50. Holtz's Influence Machine. — In construction this is a much 
simpler machine than Toepler's. It consists (Fig. 20) of two cir- 
cular glass plates face to face, one fixed, the other rotating, two 
field plates and two combs with adjustable discharging knobs. 

At the opposite extremities of 
a diameter of the fixed plate, 
window-like openings are cut 
and on the corresponding side 
of each of these openings are 
pasted the paper field plates. 
Fig. 21 represents an edgewise 
view of the machine. B is the 
rotating plate, the direction of 
its motion being indicated by 
the arrow. A is the fixed 
plate with the windows and C 
and D are the paper field plates. Extending from the field plates 
over the edge of the openings are either tongue-like strips as 
shown or else a series of sharp metal points. The operation of 
the machine in detail is as follows: 

The discharging knobs G and H are placed in contact. 




STATIC ELECTRICITY. 



35 



y 



% 



The field plate C is given a small initial charge, say positive. 
This induces a negative charge on F and repels a positive charge 
to E. B A 

An electric wind escapes from F upon B 
and, as explained in Par. 43, charges the sur- 
face of B negatively. 

The positive charge on E induces a nega- 
tive charge in D. A positive electric wind 
escapes from E upon B and neutralizes the 
negative charge brought along the surface /^y-l |£ + C 

from F. 

A positive wind escapes from the point of 
D and charges the inner surface of B posi- 
tively. As this positive charge approaches 
C a negative wind escapes from C and neu- 
tralizes it. The escape of this negative 
electricity from C leaves C more highly 
charged positively and C exerts more induc- 
tion upon F. 

This, as explained above, makes D more 
highly charged negatively and so on, the 
"building up" continuing as the plate B 
rotates. 

Finally, when the discharging knobs are TT Jy 

separated, a large positive charge is induced 
in E and a corresponding negative one in 
its knob G, while a large negative charge is 
induced in F and a corresponding positive 
one in H and the attraction between the 
two in G and H is sufficient to drive sparks 
across the gap between the knobs, this gap being much shorter 
than the distance between C and D. 

Influence machines are sensitive to atmospheric moisture but 
not to the same extent as the frictional machines, one reason being 
that the glass plates of the influence machines may be coated with 
varnish which in a measure prevents the deposition of moisture 
while in the frictional machines the plates must be kept free. 

Those influence machines which employ appropriating brushes 
are self-exciting, that is, the slight friction of these brushes is 
enough to start the machine in operation when the plate is re- 



D 



B 

Fig. 



36 ELEMENTS OF ELECTRICITY. 

volved, but the machines of the Holtz type must be given an 
initial charge. 

51. Electrical Diagrams. — The illustrations (Figs. 19 and 21) 
in the preceding paragraphs are examples of a class of figures 
termed diagrammatic which are largely used in the study of 
electricity. In these the main object is to bring out clearly the 
essential arrangements, connections and principles and to this end, 
when necessary, details are omitted, the rules of perspective are 
ignored, proportions are distorted and relative positions changed. 
Conventional signs are frequently used, a simple character stand- 
ing for a piece of apparatus like a cell or for a complicated machine 
like a dynamo. Many examples will be noticed in the following 
pages. 



STATIC ELECTRICITY. 



37 



CHAPTER 7. 



LAWS OF ELECTRIC ATTRACTION 
AND REPULSION. 

52. Coulomb's Torsion Balance. — At various points in the 
preceding pages it has been shown that charges differ from one 
another in quantity and that the force of electric attraction and of 
repulsion varies both with the quantity of the charges and with 
the distance between the charged bodies. In the present chapter 




Fig. % 



we shall see what are the laws governing this attraction and repul- 
sion and also how and by what units charges may be measured. 
The first exact experimental determinations of the laws of 
electrical attraction and repulsion were made by Coulomb with 



38 ELEMENTS OF ELECTRICITY. 

an instrument called by him the torsion balance. This is shown in 
Fig. 22 and consists of a vertical glass cylinder B graduated in 
degrees around a belt a little below its middle and covered with a 
top which is pierced with two circular openings, one in the center 
and a smaller one near the edge. Around the central opening 
stands a second and smaller vertical glass cylinder C (represented 
in the figure as being partly cut away). This smaller cylinder 
carries on its top a metal cap D graduated around its edge in 
degrees and pierced in its center with a small hole in which fits 
a metal spindle which may be turned by means of the milled head 
E. Projecting from the shoulder below the milled head is the 
pointer F which travels over the graduated edge of the cap and 
thus indicates the number of degrees through which the spindle 
has been turned. Hanging from the spindle is a delicate silver 
wire to the lower end of which there is attached so as to swing in 
the plane of the graduations a needle of shellac. At one end of 
this there is a gilded pith ball G, about four-tenths of an inch in 
diameter, and at the other end a sufficient counterweight to hold 
the needle horizontal. In the second opening in the cover of the 
larger cylinder there fits a handled stopper K from which extends 
downward a needle of shellac, or of paraffme-coated glass, ter- 
minating in a second gilded pith ball H of the exact size of the 
first. The centers of the two balls lie in the same horizontal plane. 
Finally, the instrument stands upon a bed plate A furnished with 
levelling screws by means of which the silver wire can be brought 
to coincide with the axis of the larger cylinder. 

The operation of the instrument is as follows: It is first care- 
fully levelled and then the milled head E is turned until the ball 
G is just tangent to the ball H. In this position the plane through 
the suspending silver wire and the center of the ball G passes 
through the zero of the graduated scale on the larger cylinder. K 
is now removed, a charge is imparted to H and K is then rein- 
serted. As H touches G the charge on H is distributed between 
the two balls. Having similar charges H and G repel each other 
and G (in the case represented in the figure) swings off to the right 
and as it does so twists the suspending silver wire. Now there is 
a definite law that when a body such as a wire is twisted by a force, 
its elastic limit not being exceeded, the resistance offered to the 
twisting, or the tendency to untwist, increases directly with the 
angle through which it is twisted and consequently the angle 



STATIC ELECTRICITY. 39 

through which it is twisted is directly proportional to the force 
exerted. The force which will twist a wire through ten degrees is 
exactly double that which will twist it through five degrees. As 
G moves to the right the resistance of the wire to twisting increases 
and as the distance between G and H increases the repelling force 
grows weaker until finally a position of equilibrium is reached, 
G comes to rest, and the angle through which it has turned can be 
read from the scale on the surface of the cylinder. 

53. The Law of Inverse Squares. — By means of the torsion 
balance Coulomb demonstrated that electric attraction and repul- 
sion followed the law of inverse squares, or that the force exerted 
between two charged bodies varies inversely as the square of the dis- 
tance between these bodies. Two charged bodies which at a certain 
distance repel each other with a certain force will repel each other 
with only one-fourth of this force if the distance be doubled, or 
one-ninth if it be trebled, etc. His experiment was conducted as 
follows: The balls H and G (Fig. 22) were charged as explained in 
the preceding paragraph and let us suppose that the movable ball 
G was repelled until it swung through an angle of 16 degrees. By 
turning the milled head E in the direction shown by the arrow an 
additional twist was put upon the silver wire and the ball G was 
gradually forced back towards H. When G had thus been twisted 
back to within 8 degrees of H it was found that the pointer F of 
the milled head had travelled over 56 degrees of the scale on the 
cap D. The total angular torsion on the wire was consequently 
8+56 = 64 degrees. The force exerted in the two cases was, there- 
fore, as 64 is to 16, which is the same as four to one. For small 
angles the chords bear to each other practically the same ratio as 
their arcs, hence at sixteen degrees the balls were twice as far apart 
as at eight degrees, or as the distance between the balls was divided 
by two the force between them was multiplied by 2x2 and this 
conforms to the law of inverse squares. These results are con- 
firmed by experiments based upon other methods. 

In the foregoing illustration the figures were selected to fit the 
demonstration but to obtain such accurate results in practice 
requires very careful manipulation and the observance of many 
precautions. The most troublesome source of error is loss of a 
portion of the charge during the progress of the experiment. The 
shellac needles to which the balls are fastened are non-conductors 
when free from hygroscopic moisture but a film soon deposits 



40 ELEMENTS OF ELECTRICITY. 

upon them from the air and leakage of charge results. To remedy 
this there is placed in the instrument a small saucer containing 
quicklime or calcium chloride or sulphuric acid which substances 
have a great affinity for water and thoroughly dry the air inside 
of the cylinder. 

A similar experimental demonstration can be made in the case 
of the attraction between unlike charges but the manipulation 
is much more difficult. The two balls must separately be given 
charges of the opposite kind, they attract each other and a con- 
dition of unstable equilibrium exists. Should they touch, their 
charges are neutralized and the process must be rebegun. 

From the foregoing it will be seen that electric attraction and 
repulsion follow the law of central forces. In order that the law 
of inverse squares should be strictly true, the charged bodies must 
be small spheres, so small as to approximate points, and should 
be at such distance apart that in comparison with this distance 
their own dimensions are negligible. To other bodies the law 
does not apply. The force between two charged flat discs near 
together does not vary with small variations in the distance. 

54. Variation of Force with Charges. — The force exerted between 
two charged bodies varies as the product of the charges. Reflection 
will show the truth of this second law. If two charged bodies 
repel or attract each other and the charge of either one be doubled 
or trebled, the repulsion or attraction must likewise be doubled or 
trebled. If the charge of the second one be now doubled or 
trebled, the existing force will be doubled or trebled, that is, the 
original force will be multiplied by four or six or nine. This law 
may be demonstrated by the torsion balance. It will be remem- 
bered that the two balls G and H (Fig. 22) are of exactly the same 
size, therefore, no matter what charge we start with, as soon as 
the balls have touched they (in accordance with the principle 
stated in Par. 45) divide the charge equally and we have two 
similar and equal charges. We may determine the angular repul- 
sion between these, then withdraw the fixed ball H, touch it to a 
third and equal ball thereby halving its charge, return H to the 
cylinder, determine the new angular repulsion and hence the 
variation in the repulsion with the variation in the charge. 

55. Variation of Force with Intervening Medium. — Those non- 
conducting substances which surround charged bodies and through 



STATIC ELECTRICITY. 41 

which electric effects are transmitted were termed by Faraday 
"dielectrics" The force of attraction or of repulsion between 
charged bodies varies with the nature of the dielectric. Thus two 
small similarly-charged spheres which at a certain distance apart 
in air repel each other with a force of so many dynes will, if kept 
at the same distance and immersed in oil, repel each other with a 
force only one-half as great, or, if separated by an equal thickness 
of mica will repel each other with a force only one-sixth as great. 
This is explained as follows; although there is no flow of elec- 
tricity over or through a non-conductor, the little electron systems 
of which these bodies are composed (Par. 27) are subject to the 
effects of induction and are more or less distorted, the negative 
electrons shifting to one side of the systems, the positive nucleus 
to the other. This displacement requires greater effort in some 
media than in others. When oil is the dielectric, one-half of 
the available force is spent in producing the distortion and 
hence only one-half is left to act upon the charge. With mica, 
five-sixths of the force is thus spent, leaving only one-sixth. 
The force between two charged bodies in air is not varied by com- 
pressing or by rarifying the air and for this reason and on account 
of the absence of any absolute measure we use air as our standard. 
The ratio of the force exerted between two charged bodies in a 
certain dielectric to the force exerted between the same bodies 
with the same charges at the same distance apart in air may be 
called the dielectric coefficient of repulsion and is the coefficient 
by which the force exerted between two charged bodies in air 
would be multiplied in order to obtain the force between the same 
two bodies under the same conditions in the medium to which the 
coefficient pertained. For oil this would therefore be 1/2, for 
mica 1/6, etc. 

For gases and liquids this coefficient might be determined by 
the use of Coulomb's balance as explained above but it is obvious 
that this method could not be applied to solids. However, we shall 
see later on (Par. 91) how it may be otherwise determined and at 
the same time it will be shown why it is written in the form of a 
fraction or as 1 jk. 

In problems involving forces exerted between charged bodies 
in other media than air, the appropriate value of 1 k should be 
used and when in discussions in the following pages this coefficient 
does not appear it is to be understood that the dielectric is air. 



42 ELEMENTS OF ELECTRICITY '. 

56. Unit Quantity of Electricity. — Representing by / the force 
of attraction or of repulsion, by q and q' the two charges and by 
d their distance apart we may combine the three laws discussed 
above and express them mathematically thus 

1 qXq f 



f = 



k d* 



Since, as was explained in Par. 10, electricians have agreed to 
follow the C. G. S. system of units, / in this expression must be 
measured in dynes and d in centimeters. In the torsion balance 
where the two gilded pith balls were of equal size, q and q r are 
equal, and since the dielectric is air, 1/k = 1, hence the above ex- 
pression becomes 

J d 2 

If we make the further assumption that the balls be one centi- 
meter apart, the expression reduces to 

/=9 2 

Now, if the charge q be large, the force / will be large; if it be 
small, this force will be small, that is, by varying q we can vary 
/. Suppose that q be so varied that / becomes one dyne. At 
this instant q = 1, and this unit we call the electro-static unit of 
quantity and define it as that quantity of electricity which when 
placed at a centimeter's distance in air from a similar and equal 
quantity repels it with a force of one dyne. 

Tne expression "in air" is essential to this definition as is also 
the term "electrostatic" for, as we shall see later (Par. 228), there 
is another and different unit of quantity, the coulomb, which is 
based upon current relations. The coulomb is three billion 
(3 X 10 9 ) times as large as the electrostatic unit. 



STATIC ELECTRICITY. 43 



CHAPTER 8. 

ELECTRIC FIELD. 

57. Electric Field. — We have seen that a charged body attracts 
non-electrified bodies and others with opposite charge and repels 
those with similar charge, therefore, in the space around an elec- 
trified body all bodies experience a force either of attraction or of 
repulsion and this space is called the field of the charge. As we 
recede from the charged body the force falls off rapidly and to fix 
its limits with more definiteness we define the electric field as that 
space surrounding a charged body in which the force of attraction or 
of repulsion is perceptible. If there be more than one charged body 
involved each. produces a certain effect and they have a resultant 
field. The medium within the limits of a field is not passive or 
inert but takes part in the transmission of the electrical effects 
and is subjected to certain mechanical strains. Between two 
oppositely charged bodies there is a tension as if they were being 
pulled together by invisible rubber bands and at the same time a 
stress at right angles to the bands pushing the bands apart. 

58. Intensity of Field. — It may aid the beginner in his concep- 
tion if he consider a field as analogous to a current of water. In 
the electric field there is no matter in actual movement but in a 
sense there is a flow of force and light charged bodies, such as pith 
balls, if their charges are all of one kind, will be swept along in one 
direction just as corks are carried by a river. In order that a 
charged body be acted upon it must be in the field, just as the corks 
to be carried along must be in the stream. Finally, as we may 
measure the strength of a stream by the push it exerts upon a 
board of unit area inserted in it, so we measure the strength or 
intensity of a field by the push it exerts upon a unit charge placed 
in it. We therefore define a unit field as that field which acts with 
a force of one dyne upon a unit charge placed in it. It follows from 
the deduction of Par. 56, that the field produced at a distance (/ 
in air from a charge q must be q/d 2 . In any other medium than 
air the field must be q/kd 2 . If we say that a field has a strength of 



44 



ELEMENTS OF ELECTRICITY. 



three we mean that it will pull or push such a unit charge with a 
force of three dynes. If the charge itself be not unity, the force 
with which it is acted upon is equal to the product of the charge 
by the strength of the field. 

59. Direction of Field. — Suppose that we have a horizontal sheet 
of glass in whose center there is a charged metal sphere (Fig. 23). 




Fig. 23. 

If a small pith ball be released upon the glass anywhere near the 
sphere, it will first be attracted to the sphere, will become charged 
and will then be shot away in a radial line. The force acts along 
these lines and they therefore indicate the direction of the field. 
Since opposite charges would move in opposite directions we, by 
convention, define the positive direction of a field as that direction in 
which a free positive charge would move. 




Fig. 24. 

If we continue this experiment, substituting for the single sphere 
two placed some distance apart and charged, one positively, the 
other negatively (Fig. 24), the pith ball will no longer follow 



STATIC ELECTRICITY. 



45 



rectilinear paths but curves emerging from one sphere and enter- 
ing the other. These curves indicate the direction of the resultant 
field at the successive points through which they pass. A posi- 
tively-charged ball at C is repelled by A along the line CD and 
attracted by B along the line CE. A being the nearer, the force 
CD is greater than CE and the ball moves along the resultant CF 
which indicates therefore the direction of the field at the point C. 
The space about the two spheres may be regarded as permeated 
with similar lines symmetrically distributed around the line join- 
ing the two centers. 




Fig. 25. 

Had the two spheres contained like charges, the paths would 
have been as represented in Fig. 25. 

60. Lines of Force. — These lines indicating the direction of the 
resultant electric force at the points in the field through which 
they pass are called lines of force. They start from a positively- 
charged surface and terminate upon a negatively-charged surface. 
They therefore have opposite charges at their two ends and never 
extend between bodies with like charges. They never penetrate 
below the surface or pass through a conductor. They are always 
perpendicular to the terminal surfaces at the points of origin and 
termination, otherwise there would be a component parallel to 
the surface and a movement of electricity along this surface would 
result. They never intersect, for in that case two tangents could 
be drawn at one point, that is, there could be two resultants at 
one point which is an absurdity. It follows from the foregoing 
that every electric field consists of non-conductors and is bounded 
by conductors. 

61. Graphic Representation of Intensity of Field. — In mechan- 
ics, in order to treat graphically, to discuss mathematically and 



46 ELEMENTS OF ELECTRICITY. 

to interpret geometrically problems involving parallel forces dis- 
tributed over a surface or among the particles of a mass we, by 
convention, represent the direction and the intensity of the forces 
by the direction and length respectively of a right line and for the 
entire system may substitute a single resultant whose length is 
the sum of the lengths of the separate components and whose 
point of application is the center of gravity of the surface or of 
the mass. In the case of electric fields however, the intensity 
varies from point to point and in general the lines of force are not 
parallel, therefore, instead of representing this intensity by the 
length of a resultant, we agree to represent it by the number 
of lines of force per unit of area, the area being taken perpen- 
dicular to the lines. By convention, therefore, a unit field is that 
field which contains one line of force per square centimeter of cross- 
section. 

It is not meant by this convention that in moving about in a 
unit field the force is experienced at intervals of one centimeter 
only and that the intervening space is blank, any more than by 
representing the attraction of gravity upon a body by a single line 
we imply that there is no gravity in the adjacent space. In a 
similar manner we might consider beams of light as made up of a 
number of parallel lines or rays and might agree to measure the 
intensity of the beam by the number of rays per centimeter of 
cross-section. Two beams of light passing through circles of the 
same size may differ in intensity and therefore include a different 
number of rays, yet on a cross-section of each the illumination is 
uniformly and continuously distributed, so two fields may differ 
in intensity yet in each the force exists at every point. 

In representing lines of force graphically the positive direction, 
or direction in which a free positive charge would move, should 
always be indicated by arrow-heads. 

We conclude by saying that lines of force are those imaginary 
lines in a field which by their direction indicate the direction of the 
resultant field and by their number indicate its intensity. 

62. Tubes of Force. — Another convention which avoids this 
apparent intermittent distribution of the lines of force and which 
is much used in mathematical discussions of electric fields is that 
of tubes of force. There are supposed to originate from the surface 
of a positively-charged body certain tubular surfaces various in 
cross-section and frequently curved but lying side by side like the 



STATIC ELECTRICITY. 47 

cells of a honeycomb and including within themselves all the 
space about the body. Their walls are parallel to the lines of force 
of the field and therefore at every cross-section of one of these 
tubes the same number of lines would be cut. They terminate 
upon a negatively-charged surface. If the portion of the surface 
of the charged body included in the base of the tube contains one 
unit of electricity, the tube is called a unit tube. It follows from 
this conception (and also from Par. 31) that the quantities of 
electricity upon the terminal surfaces of a tube are equal and 
opposite and a further consequence is that in the case of two 
parallel planes near together, one of which is charged, the tubes 
at a distance from the edges are parallel and the surface density 
upon the central portions of the two planes equal and of opposite 
signs. This principle is utilized in the attracted disc electrometer 
described later (Par. 101). 

It is difficult to represent these tubes graphically and we gener- 
ally do so by drawing a single line supposed to be the axis of the 
tube, so that after all we resort to lines of force. 

63. Lines of Force from Unit Charge. — If in Fig. 26 A repre- 
sents a unit charge and B a similar and equal charge at a distance 
of one centimeter from A, B will be re- ^- . 

pelled with a force of one dyne. A unit /' \ 

field is that field which acts with a force of / \ 

one dyne upon a unit charge placed in it. / ^ \ 

A is surrounded by its own field and B is j ^ (J) ° 

in it, therefore at B there is a unit field. \ / 

The same is true for every point at a dis- \ /' 

tance of one centimeter from A, that is, ^- *>**' 

the surface of a sphere with A as a center Fig. 26 - 

and a radius of one centimeter is a unit field. From Par. 61 there 
is in a unit field one line of force per square centimeter of cross- 
section. The surface of this sphere is 4?r square centimeters and 
since each contains one line of force, 4 w lines of force radiate from 
a unit charge. 

64. Gauss' Theorem. — If around one or more charged bodies 
a closed surface be drawn, the number of lines of force which 
pierce this surface is equal to 4 ?r times the total charge included 
inside the surface. This follows at once from the preceding para- 
graph. Each unit charge has 4tt lines of force radiating from it, 



48 



ELEMENTS OF ELECTRICITY. 



©• 



therefore from a charge q there would radiate 4 -n-q lines. This is 
one way of expressing Gauss' Theorem, a principle of frequent 
employment in mathematical discussions of electrostatic problems. 
An example of the application of this theorem is given in the follow- 
ing paragraph. 

65. Field about a Uniformly -Charged Sphere.— Let (Fig. 27) 
be the center of a uniformly-charged sphere, its surface density 

,*~ **v s being 8, and let P be an external point at 

/ \ a distance D from this center. Through 

\ P pass a sphere with as a center. If the 
i p charge on the original sphere be q, then 
i according to Gauss' Theorem 4 wq lines of 
/ force pierce the sphere P. The area of the 
\ / sphere P is 4 tD 2 and the distribution of 

N ^~ „-'' the lines of force is uniform, therefore the 

Fig. 27. number of lines per square centimeter is 

4 7rg/4 tD 2 , or q/D 2 . But (Par. 61) this measures the intensity of 
the field at P or, in other words, measures the force with which 
a unit charge at P is acted upon, whence we see that the charge 
upon a uniformly -charged sphere acts upon external points as if it 
were concentrated at the center. 

If the external point be indefinitely near the surface of the sphere 
the force exerted will be q/R 2 . Substituting for q its value 4 tR% 
this becomes 4tt<5, that is, the field very near the surface of a 
charged sphere is equal to iw 
times the surface density of the 
charge. Coulomb extended this 
theorem to include charged 
bodies of any shape. 

66. Field near a Uniformly- 
Charged Plane.— Let AB (Fig. 

28) be a uniformly-charged 
plane, its surface density being 
8; to find the force exerted upon 
a unit positive charge at P at a 
distance D from the plane. Let 
PC be the perpendicular from 
the point to the plane. With 
y _j_ dy describe a zone. The area of the zone is 2 wy.dy. The 




Fig. 28. 
C as a center and radii y and 



STATIC ELECTRICITY. 49 

charge upon this zone is 2 iry.dy.8. The force exerted at P by 
this charge is 

2ry.8 

z 2 

The normal component in the direction PF is 

2ir .8 .y . cos a. 



.dy 

»] 
.dy 



z z 

The integral of the components from all the zones will give the 
total force. To prepare the above expression for integration cos a 
and z 2 must be expressed in terms of y. 

From the figure z 2 = D 2 + y 2 and cos a = — = - . 

z Vl> 2 + i/ 2 

Hence df = = . dy 

V(D 2 +y 2 y 

And integrating / = - ^== + C 

Taking this between the limits y = oo and ?/ = 

/ = 2 7T<5 dynes 

In this expression D does not appear, so that the force is inde- 
pendent of the position of P with respect to the plane. If the 
charged plane be not of indefinite extent, the expression is still 
approximately correct if P be so near the plane that the dimen- 
sions of the plane as compared to this distance are very great. 

67. Force Exerted upon an Internal Point by a Uniformly- 
Charged Sphere. — Consider a uniformly-charged insulated sphere 
remote from other bodies. Let P 
(Fig. 29) be any point within such 
a sphere and let AS be any line 
drawn through this point. Let the 
tangents at A and B represent the 
traces of the tangent planes at those 
points. The line A B makes equal 
angles with these planes. With P 
as a vertex describe about PB as 
an axis a slender cone EPF. Pro- 
long its elements beyond P thus describing a second cone GPH. 
Suppose the bases of these cones to be charged, the surface density 
being the same as that of the sphere. They are similar since they 




50 ELEMENTS OF ELECTRICITY. 

have equal solid angles at the vertices and their axes make equal 
angles a with their bases. Let PB = R, PA=r, the area of the 
base EF = S, that of GH = s, the charge on EF =Q, that on GH = q. 
The force exerted by Q upon a unit charge at P is Q . sin a /R 2 , that 
exerted by q is q . sin a/r 2 . The charges on the bases of these cones 
being of the same surface density 

Q :q=S :s 
hence the above expressions are proportional to S/R 2 and s/r 2 , 
respectively. The cones being similar 

S :s = R 2 :r 2 
whence S/R 2 = s/r 2 , or the forces exerted upon P are equal and 
opposite. 

As the cones are made smaller their bases approach coincidence 
with the surface of the sphere. The whole surface of the sphere 
can be thus divided up by pairs of cones, the effects of the charges 
upon whose bases exactly neutralize one another, therefore, the 
charge upon the surface exerts no force at an internal point. 

This is true whatever the shape of the conductor or surface 
distribution of the charge but in only a few cases can the conditions 
be given a sufficiently simple mathematical expression to permit 
of ready proof. 

This fact was shown experimentally by Faraday. He con- 
structed of tin-foil and wire-netting an insulated cubical chamber 
into which he entered with his most delicate electroscopes. The 
chamber was then charged so highly that great sparks and brush 
discharges were escaping from the corners, yet his instruments 
gave no indications at all. 

68. The Charge Resides on the Surface. — The proof of the 
statement in Par. 38 that the charge resides on the surface of an 
insulated conductor follows from the foregoing. Suppose that we 
might have an insulated sphere with a charge distributed uniformly 
throughout its substance. This charge will induce on surrounding 
objects a charge of the opposite kind. The attraction between 
these charges will cause the charge in the sphere to move out to 
the surface. The portions of the charge upon the surface mutually 
repel each other and thus spread over the entire exterior. No 
part of the charge could be crowded off into the interior of the 
sphere for we have just seen that the charge on the surface exerts 
no force in the interior. 



STATIC ELECTRICITY, 51 



CHAPTER 9. 
POTENTIAL. 

69. Cause of Movement of Electric Charges. — If a charged 
conductor be connected to the earth it will be instantly discharged. 
If two equal insulated spheres containing unequal charges be 
brought into contact there will be a flow from the greater charge 
to the lesser until the two charges are equalized and equilibrium 
established. If the spheres be of unequal size yet contain equal 
charges a portion of the charge of the smaller sphere will flow to 
the larger. Finally, if these unequal spheres have charges of the 
same surface density a portion of the charge of the larger will flow 
to the smaller. The movement is therefore not entirely deter- 
mined by difference in the size of the conductors or by inequality 
either of the charges or of surface density and we naturally ask 
why does it take place. It is produced by what is designated a 
difference of electric 'potential. 

70. Physical Analogues of Electric Potential. — It has been 
remarked that one of the reasons why the study of electricity is 
difficult for the beginner is that although we have a sense of weight, 
of force, of direction, of velocity, etc., we are devoid of an electric 
sense and therefore such expressions as intensity of current, 
quantity of electricity, electric pressure, electric potential, etc., are 
pure abstractions. To convey a physical conception of these and 
to aid in our explanations we are compelled to resort to analogies. 
In explaining electric potential it is frequently compared to 
temperature and to water level. 

Making the first comparison, it is not size or shape of the bodies 
or quantity of heat contained but difference of temperature which 
determines whether heat shall pass from one body to another, the 
flow taking place from the body whose temperature is the higher. 
Thus a red-hot nail loses heat when dipped into a bucket of hot 
water, although the water may contain several hundred times 
more units of heat than the nail ; and no matter how they differ in 
size there is no net transfer of heat between two bodies at the same 



52 



ELEMENTS OF ELECTRICITY. 




Fig. 30. 



temperature. So with electricity, there is always a flow when 
conductors at different potentials are brought into contact, the 
flow (of positive electricity) taking place from the conductor of 
higher potential, and there is no flow if their potentials are the 
same. 

Again, if two vessels containing water (Fig. 30) are connected 

by a pipe there will be a flow 
from the vessel in which the 
water stands at the higher level 
and this is irrespective of the 
actual amounts of water in the 
two. There will be no flow if 
the level in the two is the 
same. 

These analogies can not be 
carried too far. For example, 
it will be noted that a change 
in temperature is accompanied by a change in volume and often 
by a change in state, but conductors show no such changes when 
their charges are varied. 

71. Mechanical Potential. — Consider a cord (Fig. 31) attached 
to a weight W and running over a pulley. By the expenditure of 
a certain amount of work on the free end of 
the cord the weight can be raised against 
the force of gravity through a vertical dis- 
tance to a new position W. In this new 
position it has a certain amount of stored up 
energy, or ability to do work, or potentiality, 
for if the free end of the cord be released the 
weight will drop back to W and in doing so 
will, if proper mechanical arrangements be 
made and losses by friction be not con- 
sidered, do as many foot-pounds of work as 
were expended originally in raising it to the 
position W. 

To raise it to W", higher than W, would 
require a greater expenditure of energy but 
also its potential energy at W" would be 
correspondingly greater than that at W. We see then that its 
potential energy, or for brevity its potential, varies with its posi- 




STATIC ELECTRICITY. 53 

tion with respect to the surface of the earth (more strictly with 
respect to the center of gravity of the earth) and at every different 
level we reach it has a corresponding different potential, always 
exactly measured by the amount of work expended in moving the 
weight from the surface of the earth to that level. 

Potential as thus explained is not an inherent property of the 
weight for in its various changes of position the weight in itself 
does not change. It sometimes becomes desirable to compare the 
potential which a body has at one point with that which it would 
have at another point and we therefore speak of the potential of 
this body at the point, or simply of the potential of the point, but 
points in space have no potential and we mean the potential which 
the body when moved to the point acquires due to the work ex- 
pended in the movement. 

In ordinary mechanical problems the force of gravity at any 
one spot is considered constant and the potential of a body varies 
directly with the vertical distance through which it is raised, 
therefore it suffices to give the height and this height in feet multi- 
plied by the weight of the body in pounds gives the foot-pounds 
by which the potential of the body is measured. However, should 
we take this force as following the law of inverse squares, the 
amount of work done in raising a body one foot from a certain 
level would differ from the amount done in raising this same body 
one foot from some other level. The relative potentials of the two 
points would not in this case be given directly by their heights but 
by the work expended in raising the same weight to the respective 
points. Logically therefore we would compare the potentials of 
points by comparing the work expended in moving a unit weight 
against the force of gravity and from the surface of the earth to 
the respective points. 

Theoretically, since it is neither raised nor lowered, no work is 
expended in moving a body about on a level. Every point on such 
a surface has the same potential and it could therefore be called 
an equipotential surface. A unit difference of potential exists 
between two levels when a unit of work must be expended in 
moving a unit weight from one to the other. 

72. Electric Potential. — We arrive at a definite conception of 
electric potential by a course of reasoning parallel to the foregoing. 
Suppose A (Fig. 32) to be a positively-charged insulated sphere 
and B a small sphere with a unit positive charge. B will be 



54 ELEMENTS OF ELECTRICITY. 

repelled by A, the force varying inversely as the square of the 
distance. At an infinite distance the force would be zero; at a 
great distance it would be very small but as the distance be- 



G- 



B 

-o 



Fig. 32. 

comes small it would increase rapidly. Should we begin with B 
at a very great distance and push it up towards A the work done 
at first would be very, very small but would increase as we ap- 
proached A and at any point as P the potential would be exactly 
measured by the work expended in bringing B up to that point. 
We therefore say that the electric potential at any point is measured 
by the amount of work that must be spent in bringing up to that 
point from an infinite distance a unit of positive electricity. Since 
we use the C. G. S. system, electric potential as thus explained is 
measured in ergs. 

Had the unit charge upon B been negative, its potential at P 
would have been negative and measured by the work expended in 
pushing it back to an infinite distance. 

From the above it follows that the difference of potential between 
any two points is measured by the work expended in moving a unit 
of positive electricity from one point to the other. Hence also, a unit 
difference of potential exists between two surfaces when it requires 
the expenditure of one erg to move a unit positive charge from one 
to the other. 

Parallel to the case of mechanical potential, a surface every 
point of which is at the same potential is an equipotential surface. 
Such a surface is that of any conductor in which no electricity is 
in movement. 

73. Zero Potential. — Electricity not being matter, we recognize 
it and measure it and its dynamical properties only by its effects. 
If all bodies about us were at the same potential there could be no 
movement of electricity among them and hence there would be 
none of the manifestations which we use in measurements. 
Repulsion of like charges depends solely upon the quantity of 
the charges, their distance apart and the medium in which they 
are situated and would be the same no matter how high or' how 
low their common potential, therefore, there is no means of 



STATIC ELECTRICITY. 55 

determining absolute potential but only relative potential, or, 
as it is usually expressed, "difference of potential." Fortunately, 
there is no need of knowing the absolute potential, just as in 
utilizing water power it is not necessary to know the height above 
the sea but it is essential to know the difference of level. A 
point at an infinite distance from all charged bodies would be at 
zero potential but for convenience the potential of the earth is 
taken as an arbitrary zero. This no more means that the abso- 
lute potential of the earth is zero than that taking the melting 
point of ice as zero implies that a lower temperature does not 
exist or the taking of the sea level as zero means that we could not 
go to greater depths. 

74. Potential at a Point due to a Charge. — If in Fig. 33 the 
charge at P be unity, that at A be Q and the distance between 

A p P ' 

0-^--G--e « 

Fig. 33. 

A and P be x centimeters, the force at P will be Q/x 2 dynes, 
the work performed by the unit charge in moving from P to P', 
a distance dx, will be 

— • dx ergs 

x 2 

and the total work performed in moving from P to an infinite dis- 
tance will be 

nx = oo 

Q 

-- -ergs 

Hence the work expended in the opposite direction in moving 
the unit charge from infinity up to P will also be Q/x ergs. But 
from Par. 72, this measures the potential at the point P. There- 
fore, the potential at any point due to a charge is equal to the 
charge divided by the distance between the charge and the 
point. 

An important corollary of the foregoing is that the potential 
at any point due to more than one charged body is equal to 
the sum of the potentials at that point due to the bodies taken 
separately. 




56 



ELEMENTS OF ELECTRICITY. 



75. Explanation of Electro -Static Induction. — If two points 
between which there exists a difference of potential be connected 
by a conductor, there will at once be a flow of electricity from 
the point of high to that of low potential, the tendency being to 
bring the two to a common potential or to obliterate the difference 
in potential between them. This principle affords us an explana- 
tion of electrification by influence as described in Par. 28. Thus, 





Fig. 33a. 



let A be an insulated sphere carrying a positive charge of elec- 
tricity. As we recede from this charge, the potential which it 
produces falls off and, (BC not yet being placed in the field of 
A), the broken circles may be taken as representing equipotential 
surfaces surrounding A, their respective potentials being indicated 
by the numbers in the diagram. Now let the elongated insulated 
conductor BC be placed in the field of A as shown. The po- 
tential of B is 4, that of C is 2, and consequently positive elec- 
tricity flows from B to C, B becomes negatively and C positively 
charged. The resultant potential of B is, from the preceding 
paragraph, that due to the positive charge on A and to its own 
negative charge, and is therefore less than 4, or say 3, and the 
equipotential surface 4 recedes to the left as shown by the dotted 
curve. Similarly, the potential of C is raised, for it is now that 
due to the charge on A and to its own positive charge. It is 
therefore greater than 2, or say 3, and the equipotential surface 
2 recedes to the right as shown by the dotted curve. The con- 
ductor BC, although with opposite charges at the opposite ends, 
is* now of a common potential and there is no further movement 
of electricity upon it. 



STATIC ELECTRICITY. 57 

76. Electro- Motive Force. — In the example of mechanical 
potential in Par. 71 above, if the cord be only partly paid out the 
weight will fall a corresponding distance, the tendency always 
being for the body to move from a point of high potential to one 
of lower. In the case of electricity there is a like tendency, and the 
insulation of a charged body may be regarded as analogous to the 
cord since it restrains the charge from flowing from the body to 
another of lower potential. If the charged body be connected to a 
body of lower potential it is analogous to paying out the cord, and 
if it be connected through a conductor to the earth the effect is 
analogous to cutting the cord. 

In the illustration of electric potential, if the little sphere 
pushed up from an infinite distance and containing the unit posi- 
tive charge be released it will be pushed back, the charge and the 
sphere both moving. If instead of releasing the sphere, it be con- 
nected, say through a conducting wire, with the earth, the charge 
alone will be pushed back along the wire to a point of zero poten- 
tial. In this case no movement of matter is involved but only of 
the charge. If new charges be supplied to the little sphere as fast 
as the previous charges flow away, it will be kept at a constant 
potential and the successive charges following along the wire will 
constitute a continuous stream. This is what is known as current 
electricity and is discussed later. 

Mechanical force is denned as that which moves or tends to 
move or tends to produce a change of motion in matter. In the 
case of the movement of electricity however no matter is involved. 
The first force might therefore be named "matter-motive force," 
the second in contra-distinction, is named "electro-motive force" 
and can be denned as that force which moves or tends to move 
electricity. It is represented in symbols as E. M. F. 

77. Practical Unit of Electro -Motive Force. — Reverting to 
our comparison of potential to water level, the flow of water is 
produced by a force and this force is the pressure due to the "head" 
or difference of level between the surface of the water and the out- 
let. So the flow of electricity is produced by the electro-motive 
force which in turn is caused by the difference of potential between 
the two ends of the path. The difference of level in the case of 
water is measured in feet, the corresponding pressure is measured 
in pounds per square inch, and for any given difference in level 



58 ELEMENTS OF ELECTRICITY. 

the pressure in pounds per square inch may be obtained by multi- 
plying this difference expressed in feet by the factor .434. In the 
case of water the cause and effect are so closely connected that we 
often hear such expressions as "a pressure of 30 feet." 

i The practical unit of electric pressure or of electro-motive force 
is called the volt and will be defined later. Difference in potential 
expressed in ergs is, for reasons given later, converted into the 
corresponding electro-motive force in volts by multiplying by 300. 
Similar to the case of water it has become usual to confound cause 
and effect and it is customary to speak of a difference of potential 
of so many volts. Some writers even go to the extent of stating 
that difference of potential and electro-motive force are two names 
for one and the same thing. In view of this, insistence upon the 
distinction becomes academic and of no practical importance and 
hereafter will not be dwelt upon. 

78. Summary. — The gist of the preceding discussion upon 
potential is that whenever a charge of electricity is produced, it 
may be regarded as brought up from infinity or from a point of 
zero potential and whenever a difference of potential is developed, 
the charge must either have been pushed against a repulsion or 
pulled against an attraction. In either case, just like a spiral 
spring which has been compressed or extended, it has a tendency 
to fly back and can be retained in its position only by a continua- 
tion of the push or pull or by the interposition of an insulator. 
The more the mechanical or chemical energy expended in bringing 
up the charge, the greater its potential energy or the greater its 
tendency to fly back when released. The potential of the charge 
is measured by the work in ergs spent in bringing up a portion of 
it equal to one positive unit. The force with which the unit 
charge when released would be pushed back, or the electro-motive 
force, is measured in units called volts whose number is obtained 
by multiplying the ergs by 300. 



STATIC ELECTRICITY. 59 



CHAPTER 10. 

ELECTROSTATIC CAPACITY. 

79. Electrostatic Capacity. — At several points in the preceding 
pages reference has been made to electric capacity. The word 
"capacity" in its application to electricity is used in a sense quite 
different from its ordinary acceptance and necessarily so, since 
in its ordinary use we usually have in mind the bulk of a solid 
or liquid which a given container will hold, while electricity, 
being devoid of geometric dimensions, can not be measured by 
volume. If by the capacity of a conductor we meant the quantity 
of electricity which could be imparted to it, the term would be 
indefinite, for as conditions vary, the same conductor could con- 
tain very different amounts. As an analogous case, it will be 
recalled that in the subject of Heat, by the "thermal capacity" 
of a body, we did not mean the quantity of heat that it could 
contain, for this varied with the size of the body, its nature and 
the temperature of the source of heat. Thus, the larger the 
body and the greater its specific heat, the more heat it would 
contain; the more it resisted change of state, disintegration or 
combustion, the higher the temperature to which it could be 
raised and consequently the more the heat that could be trans- 
ferred to it, and finally, the higher the temperature of the source 
of heat, the higher the temperature to which the body could be 
raised. We therefore agreed to define the thermal capacity of 
a body as being measured by the quantity of heat which must 
be transferred to it to raise its temperature one degree C . 

As a second analogy, suppose A and B, (Fig. 34), to be two 
steel tanks holding 10 and 5 cubic feet respectively, each supplied 
with a pressure gauge G and an inlet pipe P connected to a gas 
compressor. How musch gas will they contain? A definite 
answer can not be given, for the amount will depend upon (a) 
the size of the tanks, (b) the strength of the steel of which they 
are made, and (c) the pressure which the compressor is capable 
of producing. We might therefore agree to measure their capac- 
ity by the quantity of gas which must be pumped into them to 



60 



ELEMENTS OF ELECTRICITY. 



cause the pressure gauges to show an increase of pressure of one 
atmosphere. So, the quantity of electricity which can be im- 
parted to a conductor depends (a) upon the size (surface area) 





Fig. 34 



of the conductor, (b) upon the dielectric strength (Par. 93) of 
the surrounding medium, and (c) upon the difference of potential 
between the source from which the electricity is drawn and the 
conductor. {The non-conducting medium around the charged 
conductor prevents the escape of the charge and is therefore anal- 
ogous to the steel which prevents the escape of the gas in the 
tanks. We therefore agree that the capacity of a conductor 
is measured by the quantity of electricity which must be im- 
parted to it in order to raise its potential one unit. 

If a charge Q imparted to a body raises its potential V units, 
then a charge Q/V would raise its potential one unit. But, by 
the preceding definition, this is the measure of the capacity of the 
body, and representing the capacity by C, we have the relation 
between these three quantities given by the expression 

c = ® 

V 

80. Capacity of a Sphere. — The capacity of most bodies must 
be determined by actual measurement but for a few of simple 
geometrical form it may be calculated. The capacity of a sphere 
may be determined as follows. In Par. 74 it was shown that the 
potential at a point due to a charge Q at a distance x from the 
point is Q/x. If the charge Q be upon the surface of a sphere it 
acts as if concentrated at the center of the sphere (Par. 65), and 
hence the distance between the charge and the point must be 



STATIC ELECTRICITY. 61 

measured from the center of the sphere. Therefore, the potential 
of a point infinitely near the surface of the sphere (that is, the 
potential of the sphere itself) is V = Q/R. In other words, the 
potential of a sphere varies directly as the charge and inversely as 
the radius. In the above expression if V = 1, Q must be equal to 
R, that is, to maintain unit potential as R varies, Q must vary in 
the same ratio and preserve numerical equality with R. We also 
see that the capacity of a sphere varies directly as its radius. This 
may be shown directly by substituting in the expression for 
capacity, C=Q/V, the above value V = Q/R, whence we obtain 

C = R 

or the number of units of electricity required to raise the potential 
of a sphere by unity is equal to the number of centimeters in the 
radius of the sphere. A unit charge would therefore raise by unity 
the potential of a sphere of one centimeter radius and such a 
sphere is said to have unit capacity. 

Certain interesting consequences follow from the foregoing, two 
of which we shall now notice. 

81. Case of Two United Spheres. — If two unequal spheres be 
placed in contact or be joined by a conductor and a charge be im- 
parted to either they will come to a common potential, or will 
share the charge in proportion to their capaci- 
ties, which, from the preceding paragraph, is 
also in proportion to their radii. Suppose the 
radius of A (Fig. 35) to be twice that of B, the 
charge upon A will be twice the charge upon B. Flg - 3o - 
The surfaces of these spheres being to each other as the squares of 
their radii, the surface of A is four times that of B. The surface 
density of the charge on A is therefore as 2/4, that of the charge 
on B is as 1/1, or the surface density on B, although B has the 
smaller charge, is twice that on A. If B is very small as compared 
to A, its surface density will become very great and we have seen 
(Par. 41) that if the surface density exceeds 20 units per square 
centimeter a discharge will take place. This is the explanation 
of the action of points already described (Par. 42). 

82. Case of Two Coalescing Spheres. — Suppose two equal 
charged spheres, A and B (Fig. 36), should coalesce produc- 
ing a resultant sphere C. If the radius of A be r and that 





62 ELEMENTS OF ELECTRICITY. 

of C be R, since the volume of a sphere = %-kt z we have 

2 X |irr 3 = -|ttJ? 3 

Hence # 3 = 2 r 3 or fl = y/2 . r = 1.26 r. 

Hence, since the capacity of a sphere varies 
directly with its radius, it will require 1.26 times 
Fig. 36. as i ar ge a charge to raise the potential of the 

sphere C one unit as is required to raise that of A or of B one unit. 
But by the coalescing of the spheres C receives twice as great a 
charge as A or B, or .74 times more than necessary to bring it to 
the same potential, and hence its potential is greater than that 
of A or B. 

It is known that evaporation is accompanied by the production 
of electricity, the vapor being charged. As the vapor begins to 
condense, the molecules unite into globules, these microscopic 
globules into larger ones and these into still larger ones until drops 
of rain result. By this coalescing the potential is enormously in- 
creased until a final point is reached when a disruptive discharge, 
a flash of lightning, takes place. This is an explanation which has 
been advanced to account for thunder storms. 

83. Condensers. — In the discussion of capacity in Pars. 79 and 
80 above, the conductors were supposed to be remote from all 
other bodies. Should the conductor to which the charge is given 
be near to a second, this last being connected to the earth, a very 
different state of affairs will result. A charge imparted to the first 
will repel from the second into the earth a similar and almost equal 
charge and induce and attract into it an opposite and almost equal 
charge. In Par. 74 it was stated that the potential at a given 
point due to more than one charged body is equal to the sum of 
the potentials at that point due to the bodies taken separately. 
The potential of the first body is therefore the sum of the potentials 
due to its own charge and to the induced charge and these being of 
opposite signs the resultant potential is much less. The potential 
being less, a greater charge is required to raise the potential of the 
first body a certain amount than was required when this body was 
remote from all others, in other words, its capacity is increased. 
We see then that the capacity of a conductor is increased by the 
proximity of another which is earth connected, and since a greater 
charge can now be given to it before a given change of potential is 
produced, such an arrangement is called a condenser. The earliest 



STATIC ELECTRICITY. 63 

c orm of a condenser was the Leyden Jar which we shall now con- 
sider. 

84. Invention of the Leyden Jar. — The invention of the Leyden 
jar is in dispute, the merit having been claimed for three or more 
persons. Priestly, noted as the discoverer of oxygen, has left a 
contemporaneous account of the event which is in substance as 
follows: Dr. Muschenbroek of Leyden in experimenting with 
static electricity was much troubled by the rapidity with which 
his conductors lost their charge and ascribed this loss to some 
"effluvium" in the surrounding air. He therefore thought to pro- 
tect his charged body by surrounding it by a non-conducting 
vessel which would shield it from the atmosphere. To test this, 
he poured some water into a glass jar and holding the jar in his 
left hand he led a charge into the water by a wire attached to the 
prime conductor of the crude machine he was using. After giving 
the handle of the machine a few turns he attempted to disengage 
with his right hand the wire from the prime conductor but as he 
touched it there was a flash and he was subjected to a strong con- 
vulsive shock. In a letter describing this experience he states that 
he felt himself struck in his arms, shoulders and breast so that he 
lost his breath and was two days before he recovered from the 
effects of the blow and the terror. He added that he would not 
take a second shock for the whole Kingdom of France. 

This experiment was quickly repeated by other investigators. 
It was soon found that no appreciable charge could be given to 
the jar unless it were held in the hand and that the amount of the 
charge varied with the amount of the surface touched by the hand. 
This led to the substitution of a metallic outer covering. It was 
next discovered that the charge did not increase in proportion to 
the amount of water in the jar but rather in proportion to the area 
of the surface wetted and this led to the substitution of a lining of 
tin-foil. Finally, it was found that, other conditions being the 
same, the thinner the jar the greater the charge that it could be 
given. 

85. The Leyden Jar. — The usual form consists of a wide- 
mouthed glass jar (Fig. 37) coated inside and out for about two- 
thirds of its height with tin-foil. It is closed with a stopper of 
insulating material through which passes a brass rod terminating 
above in a knob and below in a small chain which dangles long 
enough to touch the tin-foil lining. 



64 



ELEMENTS OF ELECTRICITY. 



To charge the jar, the outer coating must be connected to earth 
either by being placed upon a wire or chain, one end of which is 
grounded, or by being held in the hand and afforded a path through 
the body. The knob is then held to the prime conductor of a 
machine in operation and in a very short while the jar is charged. 




Fig. 37. 



The inner lining receives the same kind of charge as is generated 
by the machine; the outer coating receives a charge of the opposite 
kind. It can not be charged indefinitely. As we continue to turn 
the handle of the machine, a point will be reached when the tension 
between the two opposite charges becomes so great that either the 
glass of the jar will be pierced or else a discharge will occur by the 
charge creeping up the surface of the glass to the mouth of the jar 
and thence down to the outer coating. 

A jar once charged will remain so for some time. The inner and 
outer charges are mutually bound and can not be removed by 
touching the inner or the outer coatings separately, but if they be 
touched simultaneously by any body which will afford a path 
between the two charges, the jar is instantly discharged. Since 
the effect of the discharge through the body is disagreeable and 
may be dangerous, use is made of a discharger, a knobbed con- 
ductor, hinged at the middle like a pair of tongs and furnished 
with glass handles. It is held by the handles while, as shown in 
Fig. 37, one knob is touched to the knob of the jar, the other to 
the outer coating. 



STATIC ELECTRICITY. 



65 



86. Explanation of Leyden Jar. — Reflection and experiment 
will show that the jar form of this apparatus is unimportant and 
that the essential parts are two sheets of conducting material 
separated by a thin non-conducting sheet. A window-pane set 
on edge with a sheet of tin-foil pasted in the center on each side is 
as efficient as a jar of equal area of glass and foil. Such an ar- 
rangement was called by Franklin a "fulminating pane." If more 
rigid metal sheets be substituted for the tin-foil and if they be 
mounted upon an insulating support, the glass may be replaced 
by a thin layer of air and the apparatus is then called an air 
condenser. 

The arrangement shown in Fig. 38 enables us to examine the 
action of a condenser under various conditions. A and B are 




Fig. 38. 



vertical metallic plates mounted upon insulating stands by which 
the distance between them may be varied. A is connected by a 
chain or wire to the earth and B is connected to the prime con- 
ductor C of a machine which we shall suppose is positively charged. 
At first let A be remote from B. C being at a higher potential 
than B, a charge will flow into B and B and C will reach a common 
potential. If now A be moved up near B, the charge on B will 
induce a negative charge on A and repel a positive charge into the 
earth. The potential of B is the sum of that due to its own charge 
and that due to the charge on A. This last being negative, the 
potential of B is lowered and more charge will flow into B from C 
until B and C are again brought to a common potential. Each 
additional quantity that flows into B from C will induce a eorre- 



66 



ELEMENTS OF ELECTRICITY. 



sponding quantity of negative electricity in A, the joint effect of 
the two being to reduce the potential to which B, if remote from 
A, would be raised and thus a much greater charge can be given 
to B than would otherwise have been possible. 

If the chains be now disconnected from A and from B and if A 
and B be drawn apart, the pith balls attached to the supports will 
be repelled more strongly, as if A and B had received greater 
charges. This may be explained either by the fact that as the 
distance between A and B increases, the two charges are not so 
strongly bound mutually and tend to spread, or that the effect of 
the negative charge on A upon the potential of B becomes less 
and the potential of B increases. 

If A and B be pushed closer together the pith balls will again 
drop down. The conclusion is that other things being equal the 
capacity of a condenser varies inversely as the distance apart of 
the conducting surfaces. 

87. Location of Charge of a Condenser. — In the course of 
some experiments with a Ley den jar which contained water 
instead of an inner coating of tin-foil, Franklin, having charged 
the jar, poured out the water into another vessel and expected 





Fig. 39. 

thus to obtain the liquid highly charged. His tests however giving 
no marked results, he thought to repeat the experiment and poured 
fresh water into the jar when, to his surprise, he found the jar to be 
almost as highly charged as in the beginning. He concluded that 
the charge, since it remained behind, could not have been dis- 
tributed in the liquid and must have been spread over the surface 
of the glass. To demonstrate this he constructed a jar with 
movable coatings (Fig. 39). After this jar has been charged, the 



STATIC ELECTRICITY. 67 

inner coating C may be lifted out by inserting a glass rod in the 
hook and then the glass B may be taken out of the outer coating 
A. C and A may now be shown to have no appreciable charge 
either separately or together, but if the jar be reassembled it will 
give almost as large a spark as it would have given just after 
charging. The coatings therefore serve merely as paths by which 
the charge is conducted about over the surface of the glass and 
the surface of this glass is the seat of the charge. This may also 
be shown with the condenser represented in Fig. 38 if a sheet of 
some non-conducting material be inserted between the plates but 
not if the medium between be air or gas. 

We saw in Par. 60 that every electric field consists of non- 
conductors and is bounded by conductors, and elsewhere (Par. 57) 
it was stated that the medium within the limits of a field is not 
passive or inert but takes part in the transmission of the electrical 
effects and is subjected to certain mechanical strains. Of this 
there are many proofs. For example, if a beam of polarized light 
be passed through a piece of glass not under mechanical strain no 
effect is produced but should the glass be strained, then the beam 
on emergence will, if allowed to fall upon a white surface, produce 
certain color effects. Such a beam passed through a piece of glass 
placed in an electrical field will reveal the presence of strains. 
Again, if shortly after a Leyden jar has been discharged, the dis- 
charger be again applied, an additional spark may be obtained and 
sometimes even a third. The production of this residual charge 
may be hastened by tapping the jar. This is due to the electrical 
displacements which we have seen occur within a dielectric (Par. 
55), the distortion of the little electron systems straining the 
material so near its elastic limit that, like an overloaded spring 
when the load is removed, it does not return instantly to its 
primary position. There is no residual charge in an air condenser 
Also when a Leyden jar is charged and discharged rapidly a 
number of times the glass grows warm just as does a spring when 
rapidly compressed and extended. Finally, the discharge of a 
jar, while apparently a simple phenomenon, is in reality complex 
and by the application of instantaneous photography to the 
image of the spark in a rapidly rotating mirror (Par. 688) it can 
be shown to be in the nature of an oscillation, sparks of decreasing 
intensity passing back and forth just as a released spring vibrates 
with decreasing amplitude back and forth across its neutral 



68 



ELEMENTS OF ELECTRICITY. 



position. This, with the proof that the charge of a Leyden jar 
lies on the surface of the glass, would seem to justify us in saying 
that the real seat of the charge is along the bounding surfaces of 
the non-conductor enclosed within the limits of the field and 
that the energy of the charge is due to the stresses set up in this 
medium; the conductor therefore plays a minor part. 

88. Capacity of a Spherical Condenser. — The capacity of a 
condenser is measured by the quantity of electricity that must be 
imparted to one plate (the other plate being 
connected to the earth or "grounded" and 
hence at zero potential) to raise its potential 
unity (Par. 79). For many condensers the 
capacity must be measured, for others it may 
be calculated. For example, let it be required 
to determine the capacity of a spherical con- 
denser. Let A (Fig. 40) be a metallic sphere 
surrounded by the metallic sphere B and 
separated from B by a thickness of air t. If 
R be the radius of A, that of B is R r = R + t. 
Let B be connected to earth. The potential 
of B is therefore zero. If a charge Q be im- 
parted to A, a charge — Q will be induced upon the inner surface 
of B. The potential of A due to its own charge is Q/R (Par. 80) ; 
the potential of A due to the charge on B is 

Q 

R + t 

The resultant potential of A is (Par. 74) 




Fig. 40. 



Q 



Qt 



R R + t 
And since (Par. 79) C =QV 



Qt 
R(R + t) RR' 



C = 



QRR' RR 1 

Qt t 



or the capacity varies directly as the area of the conducting sur- 
faces and, as was shown in Par. 86, inversely as the thickness of 
the layer of air separating these surfaces. 

A conducting sphere of one centimeter radius has unit capacity, 
that .is, one electrostatic unit raises its potential unity. If it be 
surrounded by a concentric conducting sphere connected to the 



STATIC ELECTRICITY. 69 

earth and leaving an air space of one millimeter (1/25 of an inch) 
between the two, its capacity becomes 11, that is, eleven units of 
electricity must now be imparted to it to raise its potential unity. 
The appropriateness of the term ' 'condenser" is hence apparent. 

89. Capacity of a Plate Condenser. — Let AB (Fig. 41) be a 
plate of glass of thickness t upon the opposite sides of which are 
pasted equal circular discs, E and F, of tin-foil, one of which, as 
F, is connected to the earth. Let the radius of these discs be R. 
If now a positive charge be imparted to E it will induce and bind 
an equal opposite charge upon F and repel into the a 

earth an equal positive charge. If the surface 
density of E be h, that of F (as shown in Par. 62) 
will be — 8. A unit positive charge placed between 
E and F will be repelled from E with a force of 
\.2irb dynes (Pars. 66 and 55) and attracted to F 
with an equal force, the total force being - k Airb. 
The work done in moving this unit charge from 
F to E, a distance t, is \ . 4 w8t. According to what 
was shown in Par. 72, this measures the difference of 
potential between F and E, hence 

v-v"=\.^u w/////m 

K Fig. 41. 

F being connected to earth, its potential V" is zero, hence the 
potential of E is 

k 
But (Par. 79) the capacity C = Q/V, hence 

£ir8t 

The face of the disc E is -n-R 2 , the charge upon it is tR-8. Sub- 
stituting this for Q in the above expression we get 

that is, the capacity of a condenser is different with different 
dielectrics and, as has already been shown, varies directly with 
the area of the conducting surfaces and inversely as their distance 
apart. 




70 ELEMENTS OF ELECTRICITY. 

90. Dielectric Capacity. — The fact that the capacity of a con- 
denser varies with the medium between the plates may be shown 
by a simple experiment. If the air condenser (Fig. 38) be charged 
to a certain potential and then, without altering the charge or the 
distance apart of the plates, a slab of paraffine be inserted between 
them, the potential will immediately drop. If mica be used the 
drop will be even greater. Since the potential is reduced the 
condenser will require a greater charge to bring it to its original 
potential, that is, by substituting for air these other media its 
capacity is increased. 

Since without changing the geometrical arrangement of a con- 
denser but by substituting one dielectric for another we alter its 
capacity, and since we have seen that the charge resides on this 
dielectric and not on the conducting plates, we naturally associate 
the idea of capacity with the dielectric itself and therefore speak 
of dielectric capacity. We use air as the standard of comparison 
and when we say that the dielectric capacity of mica is six we mean 
that a condenser in which mica is the dielectric has six times the 
capacity of one with air as the dielectric but otherwise precisely 
similar. The dielectric capacity of a substance is therefore meas- 
ured by the ratio of the capacity of a condenser in which the sub- 
stance is employed as the dielectric to that of the same condenser 
in which air has been substituted for the substance. This ratio is 
represented by k in the last expression in the preceding paragraph. 
This factor k is sometimes called the dielectric coefficient since it 
is the coefficient by which the capacity of an air condenser must 
be multiplied to obtain the capacity of the same condenser in 
which the corresponding dielectric has been substituted for air. 
Reference to Par. 55 will show that this is the reciprocal of what 
was there called the "dielectric coefficient of repulsion/' whence 
it follows that in a medium whose dielectric coefficient is k, the 
force exerted between charged bodies is |th as much as the force 
exerted between these bodies in air. 

91. Determination of Dielectric Capacity. — In Faraday's deter- 
mination of dielectric capacity he used spherical condensers 
similar to the one represented in Fig. 40 but with the opening in 
the outer sphere closed by an insulating stopper through which 
the stem of the inner sphere passed. The outer sphere was sup- 
plied with a stop cock by which the air between the spheres could 
be drawn off and liquids or gases introduced, also the outer sphere 



STATIC ELECTRICITY. 71 

could be separated into halves when it became necessary in in- 
serting or removing other materials. Two of these condensers of 
equal size were taken. In one air was retained as the dielectric; 
into the other was introduced the substance whose dielectric 
capacity was to be determined. Suppose the space in the second 
one to be filled with oil. The air condenser was now charged to a 
certain potential which was carefully measured by the torsion 
balance. The outer coatings of the two condensers were next 
placed in contact, either directly or through a third body, and were 
thus brought to a common potential. Finally, the inner coatings 
were brought into contact. The air condenser, being at a higher 
potential, gave up a portion of its charge to the oil condenser until 
equality of potential was reached. If the capacities of the two 
condensers were equal, the charge would be divided equally 
between them and the resultant potential would be one-half that 
of the original potential. If the capacity of the oil condenser were 
greater than that of the air condenser, the oil condenser would take 
more than half the charge and the resultant potential would be 
less than half the original potential. If the capacity of the oil 
condenser were less than that of the air condenser, the resultant 
potential would be greater than one-half of the original. In either 
case, the resultant potential having been measured, the dielectric 
capacity is calculated as follows. Let Q be the original charge of 
the air condenser, V its original potential, V the potential of both 
condensers after division of the charge, C their capacity when 
used as air condensers and k the dielectric capacity of the oil. 
From Par. 79 we have 

C=^, whence Q = VC 

The charge in the air condenser after contact is 

Q' = V'C 

The charge in the oil condenser is 

Q" = k(V'C) 

The sum of the separate charges must be equal to the original 
charge, hence 

VC = V'C+fc(V'C) 
whence 

. V-V 

k = T77 



72 ELEMENTS OF ELECTRICITY. 

92. Dielectric Capacity of Various Substances. — The dielectric 
capacity of many insulating materials has been measured and some 
of the accepted determinations are given in the table below. 
There is wide variation in the results obtained by different inves- 
tigators and this is due to the fact that the capacity of a condenser 
is greater if the charge be slowly imparted than if it be suddenly 
applied and as suddenly withdrawn, in the first case the medium 
yields and accommodates itself to the stress put upon it. By the 
so-called, instantaneous method of determining dielectric capacity, 
the condenser is charged and discharged several hundred times per 
second and the determinations are less than those obtained by the 
slow methods. The dielectric capacity of a vacuum is about .94; 
that of the various gases differs from that of air in the third or 
fourth decimal place only. 

Table of Dielectric Capacities. 



Paper 


1.5 


Mica 


4.0 to 8 


Beeswax 


1.8 


Porcelain 


4.4 


Paraffine 


2.0 to 2.3 


Glycerine 


16.5 


Petroleum 


2.0 to 2.4 


Ethyl Alcohol 


22.0 


Ebonite 


2.0 to 3.2 


Methyl Alcohol 


32.5 


Rubber 


2.2 to 2.5 


Formic Acid 


57.0 


Shellac 


2.7 to 3.6 


Water 


80.0 


Glass 


3.0 to 10. 


Hydrocyanic Acid 


95.0 



93. Dielectric Strength. — The quantity of electricity which 
must be imparted to a condenser to raise its potential unity de- 
pends upon the capacity of the condenser. If the plates of a con- 
denser be connected to two objects between which unit difference 
of potential is maintained, the condenser will receive the charge 
which is the measure of its capacity. If the difference of potential 
between the two objects be doubled, the condenser will receive a 
charge twice as great and so on. In other words, as has been 
stated in Par. 79, the quantity of electricity which can be trans- 
ferred to a condenser depends upon its capacity and also upon the 
difference of potential maintained between the two plates. By 
increasing this difference of potential, a greater and greater charge 
can be given to the condenser but this can not go on indefinitely 
for as the potential increases, the strain upon the dielectric in- 
creases until finally it is pierced by a spark and the condenser is 
discharged. The resistance which a medium offers to piercing by 



STATIC ELECTRICITY. 



73 



the spark is called its dielectric strength and is measured by the 
maximum difference in potential in volts which a given thickness 
(one centimeter) of the medium will stand before piercing occurs. 
It is difficult of accurate determination since it is affected by 
temperature and pressure, by the size and shape of the bodies 
between which the sparks pass and by the manner in which the 
electric pressure is applied, that is whether constantly in one 
direction or alternately in opposite directions. 

The dielectric strength of air has been investigated by a number 
of observers. A minimum difference of potential of 300 volts is 
required to produce a spark at all, even across a space of less than 
.01 of an inch. Sparks pass more readily between points than 
between bodies of other shapes. The strength increases with the 
density of the air, whether produced by falling temperature or by 
increasing barometric pressure. If air be under a pressure of 500 
pounds per square inch, it can be hardly pierced at all. On the 
other hand, a vacuum offers an equal resistance. To throw a 
spark between two points an inch apart requires about 20,000 
volts and to produce a 15-inch spark requires 145,000 volts. To 
pierce one centimeter of paraffine requires 130,000 volts, one 
centimeter of ebonite about 200,000 and one centimeter of mica 
about 350,000. 

94. Commercial Condensers. — Condensers are used, as will be 
explained later, in certain electrical measurements, in telegraphy 



KVWW^V^^^ 




pa^a^^a^a 




Fig. 42. 



and in the production of high potential electricity by means of 
induction coils. They are usually constructed of alternate layers 
of tin-foil and mica or of tin-foil and waxed paper pressed tightly 
together and thus including a large surface in very small bulk. 
The alternate sheets of foil are connected as shown diagrammat- 
ically in Fig. 42 (in which the shaded spaces represent the paper 



74 ELEMENTS OF ELECTRICITY. 

and the heavy lines the foil) and the whole is contained in a rect- 
angular or cylindrical case provided with the proper terminals. 
The one represented in the figure is of invariable capacity but by 
connecting the sheets of foil together in groups attached to separate 
terminals it is possible to use at will different fractions of the entire 
condenser. 

95. Practical Unit of Capacity. — The practical unit of capacity, 
the farad, is denned as the capacity of that body whose potential 
is raised one volt by one coulomb of electricity. The coulomb will 
be denned later (Par. 228) but we have already seen (Par. 56) that 
it is three billion (3 X 10 9 ) times as large as the electrostatic unit 
of quantity. We have also seen (Par. 77) that the electrostatic 
unit of potential is equal to 300 volts. Since one electrostatic unit 
of quantity raises the potential of a sphere of one centimeter radius 
300 volts, one coulomb would raise the potential of such a sphere 
to 3X10 9 X300, or nine hundred billion (9X10 11 ) volts, and a 
sphere of 9 X 10 11 centimeters radius would be raised one volt by 
one coulomb and would therefore have a capacity of one farad. 
The radius of such a sphere is about 5,600,000 miles or about 
1,400 times as large as that of the earth. A farad is therefore so 
great that in practice one-millionth of a farad (or a micro-farad) 
is used. An isolated sphere of 9X10 5 centimeters radius (about 
5.6 miles) would have a capacity of one micro-farad. A mica-tin- 
foil condenser containing about 25 square feet of tin-foil, has also 
a capacity of about one micro-farad. 

Since a sphere of 9X10 5 centimeters radius has a capacity of 
one micro-farad, a sphere of one centimeter radius (or a sphere 
of unit electrostatic capacity) has a capacity of 
1 1 



9 X 10 5 900,000 



micro-farad 



96. Work Expended in Charging a Condenser. — In Par. 72 it 

was shown that the potential at a point was measured by the work 
done in bringing up to that point from an infinite distance, or from 
a point of zero potential, a unit charge. If the potential be V, we 
mean that the work done in bringing up the unit charge is V ergs. 
The work done in bringing up a charge Q would therefore be QV 
ergs, although the potential of the point would still remain V, that 
is, the assumption is that the charge brought up does not increase 
the potential of the point. The potential in this case is analogous 



STATIC ELECTRICITY. 75 

to the head of a body of water which body is of such extent that 
its level is not appreciably altered by the pumping up of additional 
quantities. However, the case is different if the charge is to be 
brought up to a body of limited capacity. Suppose we have a 
sphere of unit capacity and at zero potential. At first sight it 
might seem that to transfer to this sphere from zero potential a 
certain charge would not require the expenditure of any energy. 
But suppose the charge to be brought up by successive portions. 
The first portion could be brought up without the expenditure of 
energy but would raise the potential of the sphere and would repel 
the second portion as the latter approached. These two portions 
would repel the third still more strongly and so on, the work re- 
quired to bring up the successive portions increasing in regular 
progression. The potential in this second case is analogous to the 
head of water in a narrow vessel, each portion that is added raising 
the level and thus increasing the work which must be expended to 
bring up the succeeding portion. 

In charging such a body, its potential being zero at the outset 
and V ergs at the close, the average potential is only \ V, and 
the work done is therefore 

iQV ergs. 

97. Energy of a Condenser.— If the body to which the charge 
is brought is of capacity C instead of unity, the expression \QV, 
since Q = VC, may be put in the form \ Q 2 /C, that is, if a charge 
Q be given to a condenser of capacity C, the work spent is propor- 
tional to the square of the charge and inversely proportional to the 
capacity of the condenser. 

If the condenser be discharged it will give out as much energy 
as was expended in charging it and therefore the expression 
hQ 2 /C also represents the energy of discharge or the energy of 
the condenser. 

If for Q we substitute its value VC, the expression becomes 

h VC 

that is, the energy of a condenser varies as the square of its 
potential and as its capacity. This principle is utilized in the 
quadrant electrometer (Par. 103), and is also of great importance 
in radio-communication, since, as will be shown later, the distance 



76 ELEMENTS OF ELECTRICITY. 

which may be attained varies with the amount of energy thrown 
off at the origin in the form of waves and these waves are com- 
monly produced by the discharge of a condenser. 



STATIC ELECTRICITY. 77 



CHAPTER 11. 

ELECTROSTATIC MEASUREMENTS. 

98. Electrostatic Measurements. — The electrostatic quantities 
which we most frequently desire to measure are quantity of charge 
and difference of potential. Of these two, the latter is the more 
important but if we may measure either one we may determine 
the other indirectly. Thus, if an unknown charge raises the 
potential of a certain conductor by a given amount, we have only 
to find out how much its potential is raised by a unit charge and 
can then determine at once the quantity of the unknown charge, 
or similarly, can determine the potential to which a known charge 
will raise a given conductor. 

99. Unit Jars. — At first, attempts were made to measure 
charges directly by means of what were called "unit jars." These 
were small Leyden jars, their outer coatings connected with a 
knob which could be made to approach or recede from the knob 
communicating with the inner lining. By adjusting the air gap 
between these knobs a greater or a lesser charge could be given 
to the jar before a discharge took place. They were used to 
measure the charge imparted by a machine to a large Leyden jar 
or to a battery of these jars. One was inserted between the 
machine and the knob of the large jar. Obviously no charge could 
pass to the large jar until the unit jar ^^^ 
filled up and discharged and the amount 
was determined by counting the num- 
ber of sparks. ( J\ 

100. Principle of Electrometers. — 

Instruments for measuring differences 
of electrostatic potential are called elec- 
trometers. The principle upon which 
they operate will be understood from 
the following. Suppose A and B (Fig. 

43) to be two bodies between which there exists a difference of 
electrostatic potential which we desire to measure. For one reason 




78 ELEMENTS OF ELECTRICITY. 

or another it is generally impracticable to measure the difference 
of potential between the bodies themselves and we therefore have 
to transfer the potentials to the parts of our instrument. Let C and 
D be two small spheres, D fixed and C attached to a spring which 
can be extended or compressed and which has a scale from which the 
force producing the extension or the compression can be read. If 
A and C be connected by a wire they will at once attain the same 
potential and the charge imparted to C will vary directly with the 
potential of A. Likewise if B be connected with D, D will attain 
the potential of B and acquire a charge proportional to this 
potential. C and D will now attract or repel each other with a 
lorce which can be read from the scale and which is proportional 
to the product of the charges which in turn are proportional to 
the potentials. But C and D are of the same potentials as A and 
B, respectively, and therefore this force is proportional to some 
function of the difference of potential between A and B. If 
A or B be very small, they would part with a considerable portion 
of their charge when connected to C and D and the resultant 
potential would be less than the original potential, but usually 
A and B are so large that the small loss of potential can be neg- 
lected. For example, B is frequently the earth, in which case D 
is of zero potential. 

Coulomb's torsion balance, already described, may be used as 
an electrometer, the removable ball being touched to the body 
whose potential is required and thus obtaining a charge propor- 
tional to that potential, but the usual form of electrometers use 
plates or flat moving parts instead of the spheres described above. 

101. The Attracted Disc Electrometer. — The attracted disc 
electrometer was invented by Snow Harris but perfected by Lord 
Kelvin. Its essential parts are shown diagrammatically in Fig. 44. 
AS is a lever pivoted upon a tightly stretched horizontal wire CD. 
At one end is a counterpoise B, at the other end a fork A which 
embraces an upright E and across which there is stretched a fine 
hair. From the fork there is suspended so as to hang horizontally 
a circular disc G which moves with a minimum clearance inside of 
a fixed ring R. A portion of this ring is represented in the diagram 
as cut away. Below the disc and ring is a circular plate P insu- 
lated by being mounted upon a glass stem which in turn is attached 
to a brass support. The plate P can be raised or lowered by turn- 
ing the micrometer screw H, which is so arranged that the plate 



STATIC ELECTRICITY. 



79 



is always kept strictly parallel to the disc G and which permits the 
distance through which P has been moved to be read with great 
accuracy. Upon the upright E there are two black dots and when 
the lower surface of G is exactly in the plane of the lower surface 




Fig. 44. 

of R the hair at A is just between these dots. There is a lens L 
by which the position of the hair is observed and it is said that an 
error of as little as 1/50,000 of an inch can be detected and cor- 
rected. G and R are connected electrically by means of a wire from 
R to D. By moving the counterpoise B or by twisting the wire 
CD, the disc G is given an initial position slightly above the ring 
R. Small weights are then placed upon G until the lower surfaces 
of G and R lie in a common plane. From the weights used the 
force in dynes to effect this is determined. The weights are then 
removed. If now a charge be given to G it will induce an opposite 
charge in P, G and P will attract each other and G will be drawn 
downward. By varying the position of P the downward pull on 
G can be so adjusted that the plane of the lower surface of G coin- 
cides with that of the lower surface of R. At this point, the force 
of attraction equals the force in dynes as determined by the weights 

102. Theory of Attracted Disc Electrometer. — In Par. 40 we 
saw that a charge imparted to a flat disc was uniformly distributed 
over the central portion but much denser around the edges. When 
G and R are in one plane they practically constitute one surface. 
The surface density over the movable disc G is therefore quite 
uniform and the excessive density is confined to the fixed ring R 
which on this account was called by Lord Kelvin the "guard ring." 



80 ELEMENTS OF ELECTRICITY. 

To measure the difference in potential between two bodies, R 
(and hence G) is connected to one and P to the other. Let V be 
the potential of P and V" that of G. The surface density of G 
is 8 and that of the induced charge upon P is — 5. The difference 
of potential, V' — V", is measured (Par. 72) by the amount of 
work done in moving a unit positive charge from P to G, a dis- 
tance D. The force exerted upon a unit charge placed between 
P and G is (Par. 66) an attraction of 2 tt8 by one and a repulsion 
of 2 7r5 by the other, or a total force of 4 tt<5. The work therefore is 

V - V" =At8D 

Again, every unit charge upon G is attracted by P with a force 
of 2 7r<5 dynes. If £ be the area of G, the charge upon G is Sb and 
the total force of attraction is 

F = 2tt8-S 



Whence / p 

S = V 2^S 
Substituting in the expression for V — V", we have 



y-V" = Dy^f 

F is determined in dynes from the weights as described above, 
D is in centimeters, S is in square centimeters and V — V" ', the 
difference in potential, is in absolute electrostatic units. As 
explained in Par. 77, if this be multiplied by 300 it is converted 
into volts. 

Since S is constant and F may be kept constant, the expression 

/StF 
y — ^— is a constant and can be determined once for all. The 

difference of potential between G and P is therefore directly pro- 
portional to the distance between the plates when the instrument 
is balanced. 

The actual distance between the plates is difficult of measure- 
ment. If P be connected to some other charged body whose 
potential is V" and the apparatus be balanced we have 



V S 

Subtracting this from the expression above we have 



V - V" = (£>-£)') \/^f 



F 

S 



STATIC ELECTRICITY. 



81 



that is, the difference of potential between two charged bodies, 
each being compared to a third, is proportional to the difference 
in the distance between the plates in the two observations and 
this difference in distance is easily and accurately determined from 
the micrometer screw. 

By using the earth as the third body, that is, by connecting G 
to the earth, V" in the above becomes zero. 

There are many refinements used in connection with this instru- 
ment but it is not necessary to describe them here. 

103. The Quadrant Electrometer.— The quadrant electrom- 
eter of Lord Kelvin is a more sensitive instrument than the 




Fig. 45. 

foregoing. It is shown diagrammatically in Fig. 45. A flat 
cylindrical brass box is cut into quadrants A, B, C and D (this 
last is represented as cut away to show the interior") which are 
fastened to the top of the apparatus (not shown) by the glass 
pillars E, F, etc. The diametrically opposite quadrants A -C and 



82 ELEMENTS OF ELECTRICITY. 

B — D are connected by wires (Fig. 46). Within the box is a flat 
needle N of light aluminum plate which is fastened rigidly to an 
aluminum wire extending above and below. The needle is sus- 
pended by one or by two fibres of silk or by a single fibre of quartz 
L attached to the upper end of this wire. To the lower end of the 
wire there is fastened a platinum wire which dips into some sul- 
phuric acid in a glass jar. This jar, which also serves as a case for 
the lower part of the instrument, has an outer coating of tin-foil 
and with the sulphuric acid within is thus a Ley den jar. The 
acid also keeps the air in the jar dry and prevents loss of charge by 
moisture. The needle swings midway between the top and bottom 
of the box and symmetrically over the separation between the 
quadrants. Upon the wire above the needle there is fastened a 
small circular concave mirror M. The angle through which the 
needle turns is determined either by the reflection of a beam of 
light from this mirror upon a scale or by observing in the mirror 
by means of a telescope the reflection of a printed scale fastened 
just above the telescope. These methods of determining the angle 
of deflection are described in detail later on; the former in connec- 
tion with the mirror galvanometer (Par. 377), the latter in con- 
nection with the suspended coil galvanometer (Par. 378) . There 
project from the glass case terminals, called "electrodes, " one of 
which connects with each pair of quadrants and one with the acid 
of the jar. 

To use the instrument, one pair of quadrants is connected to 
one body, the other pair to the second body between which the 
difference of potential is to be measured. The quadrants thus 
acquire the potentials of the respective bodies. 
The Ley den jar is then charged until the needle 
has a high potential Y 3 which by certain arrange- 
ments, not necessary to describe here, is kept 
constant during the measurement. If the 
charges are of the same kind, mutual repulsion 
exists between the charge on the needle and 
those on the adjacent quadrants and the needle 
moves toward the quadrant of lesser charge, that is, of lower po- 
tential. The deflection of the needle is read from the mirror and 
the difference of potential is proportional to this deflection. 

This instrument is sufficiently delicate to measure differences 
of potential almost as small as .01 of a volt. 




STATIC ELECTRICITY. 83 

104. Theory of the Quadrant Electrometer. — Figure 47 repre- 
sents a cross-section of the needle and two adjacent quadrants, 
the potentials being as marked and V 3 being much greater than 
either of the others. Vi V 3 
constitute a condenser, V 2 V 3 
another. The energy of a con- 
denser (Par. 97) is JY 2 C in 
which V is the difference in 
potential between the two Fl §- 47 - 

plates and C is its capacity. The energy of Vi Y 3 is thereiore 

iC(V 3 -Vi) 2 
and that of V 2 V 3 is 



iC(V 3 -V 2 ) 



y 3 being symmetrically suspended with respect to Vi and V 2 as 
it swings to the right or left it increases the surface. embraced by 
one by exactly the same amount as it decreases the surface em- 
braced by the other and as its edges still remain well inside of 
Vi and y 2 it increases the capacity of one condenser and decreases 
by an equal amount that of the other. Let this increment of 
capacity for a unit angular motion of V 3 be denoted by k; the 
decrement will be —k. The change in the energy of Vi V 3 for an 
angular movement 6 will therefore be \kd (V z — Vi) 2 and that 
of y 2 V 3 will be -ikd(V 3 -V 2 y. The total change in the 
energy of the system will be 

ikd(v 3 -v 1 y-ike(v 3 -v 2 y 

The force moving the needle = — rrp- = — ^=- is therefore 

F= p(y 3 -y 1 ) 2 -p(y 3 -y 2 ) 2 

or the force between the needle and each quadrant is proportional 
to the square of the difference of potential between the needle and 
the respective quadrant. 

Simplifying the foregoing expression we have 

yi+y 2 \ 



fc(y 2 -yi)(y 3 



or the force tending to turn the needle is proportional to the 
difference of potential between the quadrants and also to the 
difference between the potential of the needle and the average of 
the potentials of the two quadrants. 



84 ELEMENTS OF ELECTRICITY. 

Since V 3 is kept constant and is very large as compared to V 
and V 2 , ( V 3 — - J —^ — -) may be taken as a constant and the ex' 



2 
pression for the force becomes 

F = a(V 1 -V 2 ) 

The force being counterbalanced by the torsion of the sus- 
pending fibre, the difference of potential, V x — V 2 , between the 
two bodies being examined is proportional to the deflection as 
indicated by the mirror. By using a known difference of potential 
the constant a may be determined once for all. 



MAGNETISM. 85 



PART II. 
MAGNETISM. 



CHAPTER 12. 
MAGNETS. 



105. Natural Magnets. — Of the four important ores of iron the 
richest is that one whose chemical formula is Fe 3 4 . This when 
pure is a heavy black mineral, often coarsely crystalline but also 
frequently massive. It occurs in beds in many widely scattered 
localities and from it a large part of the iron and steel of commerce 
is made. Some specimens of this ore possess the remarkable 
property of attracting and picking up small particles of iron and 
steel. If such a specimen be dipped or rolled in iron filings, the 
filings will adhere to it like a mossy growth. This property has 
been known for nearly 3,000 years and because the best speci- 
mens came from the vicinity of the town of Magnesia in Lydia 
they were called by the Greeks magnetis lithos (Magnesian or 
Magnetian stone), whence are derived our name magnet and the 
mineralogical term magnetite or magnetic iron ore. To distinguish 
these magnets from those prepared artificially they are usually 
called native or natural magnets. 

106. Lodestones. — About 800 years ago an additional property 
of magnets, equally as remarkable as the first, became known to 
European nations. If an oblong or elongated magnet be arranged 
so that it is free to rotate in a horizontal plane (as for example by 
suspending it by a thread or by placing it upon a floating cork or 
by balancing it upon a pivot) it will take up a north and south 
position, the same end always returning to the north, no matter 
what may be its primary position. This property was quickly 
utilized in navigation and since these magnets thus led the 
mariner about over the seas, they were called lodestones (leading 
stones) . 



86 ELEMENTS OF ELECTRICITY. 

107. Fables of the Ancients. — In contemplating the mystical 
power of attraction of magnets, the ancients gave free rein to their 
imagination and gravely recorded and copied from each other's 
writings the most wonderful statements about magnets. They 
were by some reputed to be endowed with life and to possess a 
soul. A magnet was supposed to protect from witchcraft. If 
held in the hand it cured cramps. The power of a weakening 
magnet could be restored by soaking it in the blood of a buck 
while if it were rubbed with garlic it lost its power. It also lost 
its power when in the presence of a diamond. If pickled in salt 
with a certain fish, the remora or sucking fish, it acquired the 
property of attracting gold and silver and could thus be used to 
fish up treasure from the deepest wells. At various points in the 
Eastern Seas were islands of lodestone so powerful that they pulled 
the nails from the sides of vessels and thus caused their loss. In 
those parts ships had to be built with wooden pegs. In India 
there were side by side two mountains, one of lodestone so power- 
ful that if a person with iron nails in his shoes stepped upon it he 
could not raise his feet to take a second step, the other of a sub- 
stance which repelled iron so strongly that such a person found it 
impossible to place his foot upon the surface. We can not now 
understand the state of mind of these writers, for very simple 
experiments would have readily shown the absurdity of their 
statements. 

108. Doctor Gilbert. — Such for near 2,000 years remained the 
state of knowledge until, as has already been stated (Par. 12), a 
certain Doctor Gilbert in the reign of Queen Elizabeth undertook 
a series of investigations of the properties of the lodestone. In 
1600 he published his work, De Magnete Magneticisque Corporibus 
(On the Magnet and Magnetic Bodies), in which he described his 
experiments, wonderful for their simplicity and in some directions 
well nigh exhaustive. Anticipating the Baconian system, he 
accepted no statements about magnets until he had confirmed 
these statements by his own experiments and he was thus able 
not only to sweep aside the mythological rubbish which until then 
passed current but also to bring forward many facts, hitherto 
unknown. In short, by his researches he brought to light the 
majority of the truths and principles upon which our present 
knowledge of magnetism is based. 



MAGNETISM. 



87 




109. Artificial Magnets. — If a bar of iron or of steel be rubbed 
or stroked in a certain manner (see Par. 162) by a lodestone, the 
bar acquires magnetic properties. Steel is found to be more reten- 
tive of magnetism than iron and is accordingly used. The bar 
thus magnetized may in turn be used to produce magnetism in 
others. There is another and better method, in which an electric 
current is used to produce magnets, but an explanation of this 
method must be deferred until later (Par. 164). These artificial 
magnets, on account of their strength, of the ease with which they 
may be prepared and of the 
readiness with which they may 
be given any desired shape, 
have quite displaced lodestones 
and are the ones referred to in 
the following pages. The com- 
monest forms are bars and the 

so-called needles. These last ^^zz^- Fig. 48. 

are usually thin, elongated, losenge-shaped magnets with a socket 
at the center by which they may be pivoted upon a sharp point 
(Fig. 48). In the best needles the socket is jewelled. 

110. Magnetic Poles. — In pursuing a certain line of investi- 
gation, Gilbert caused to be cut from a lodestone a regular sphere 
to which he applied the name terrella (little globe). When this 
terrella was rolled in iron filings they adhered to it in tufts, not 
however uniformly over its surface but upon two restricted areas 
at the opposite ends of a diameter. These regions he designated 
as the 'poles of the terrella. 

If a bar magnet or a magnetic needle be dipped in filings, they 
will adhere only to the regions at the ends, and these regions are 

jyj likewise called poles. 

If such a magnet be balanced 

upon a cork which in turn floats 

in a vessel of water (Fig. 49^ 

it will oscillate in a horizontal 

plane and finally come to rest 

in a north and south position. 

The same end of the magnet. 

Fig. 49. always points north and is 

therefore called the north pole, the other end being called the 

south pole. The fact that this one end always points north shows 




88 



ELEMENTS OF ELECTRICITY. 



that it must differ from the other, but so far as the attraction 
of iron filings and the lifting of iron weights is concerned, the two 
ends are of identical properties. The north and the south poles 
are frequently designated positive and negative, respectively. 

111. The Poles Inseparable. — Should a slender bar magnet 
(Fig. 50) be broken in half, it will be found that each half is a 
complete magnet and has a north and a south pole nearly as 



3 £ 



~7 £ 



Fig. 50. 

strong as those of the original magnet. If one of these halves be 
again broken, the fragments will each have a north and a south 
pole and so on. In other words, it is impossible to get a separate 
north or south pole unaccompanied by an equal pole of the oppo- 
site kind. Explanation of this fact will be given later (Par. 152). 

112. Magnetic Attraction. — If a bar magnet be dipped into 
iron or steel filings and then be lifted, the filings will be found to 




Fig. 51. 

cling to it like a thick mossy growth (Fig. 51). Upon examination 
the following peculiarities will be noted. 

1st. As already stated, the filings do not adhere all over but 
mainly in the region of the poles and none at all in the central 
portion of the magnet. 

2nd. The individual filings cling to the magnet by their ends 
rather than by their sides and at each pole radiate from an internal 
focus near the end of the magnet. 

3rd. The filings cluster more thickly along the edges and corners 
of the magnet than along the flat surfaces. 



MAGNETISM. 



89 



4th. Where the filings are thickest, it will be found that those 
which cling to the magnet may have others clinging to them in 
turn, and these may have still others, forming, as it were, chains. 

113. The Attraction Takes Place Through Intervening Bodies. 

— The magnetic attraction takes place at a distance and through 
space, although it falls off rapidly as the distance increases. Fine 
filings will leap up to reach a strong magnet held above them. 
Furthermore, the attraction is propagated through intervening 
objects. A bar magnet inserted in a glass tube will attract filings 
through the glass. If filings be sprinkled upon a thin board or a 
slate or a sheet of glass or of brass, a magnet moved about beneath 
will drag after it the filings on top. There is but one screen for 
the magnetic force and that, as will be explained later (Par. 143), 
is a comparatively thick plate of iron or steel. 

114. The Attraction Mutual. — If a small iron bar be floated 
upon a cork in a basin of water, the bar and cork will move about 
in pursuit of a magnet held near. If the bar and the magnet be 
made to change places, the magnet will follow about after the iron 
bar. 

115. Action of Magnets upon Each Other. — The mutual action 
of magnets is most easily studied by means of a magnetic needle. 
If when the needle has come to rest, its north end be approached 




Fig. 52. 

by the north end of a bar magnet (Fig. 52), it will be repelled and 
move off. On the other hand, its south end will be attracted by 
the north end of the magnet. If the bar magnet be turned end 
for end and its south end be held to the north end of the needle, 
the latter will be attracted, and if it be held to the south end. this 
end will be repelled. We see then that magnetic poles follow a law 



90 ELEMENTS OF ELECTRICITY. 

similar to that given for positive and negative charges of elec- 
tricity (Par. 24), that is, like poles repel and unlike poles attract 
each other. 

If two bars of similar shape and size attract each other we 
would know that one of them was a magnet but without other 
test could not tell which. If they repelled each other we would 
know that they were both magnets. 

116. Why a Magnetic Needle Points North and South. — Sup- 
pose that upon a bar magnet resting on a horizontal surface there 

be placed, as shown in Fig. 
53, a magnetic needle. The 
north pole of the magnet 
will repel the north pole of 
the needle but will attract 
its south pole; the south pole 
of the magnet will repel the 




Fig. 53. 



south pole of the needle and attract its north pole. The needle 
will in consequence take up a position parallel to the axis of the 
bar magnet but with its poles in reverse direction. Similar experi- 
ments led Gilbert to the discovery that the earth itself is an immense 
magnet, its poles being in the neighborhood of, but not coinciding 
exactly with, the geographical poles. A magnetic needle will 
therefore take up a position approximately in the plane of the 
earth's magnetic axis for the same reason that the needle in 
the above experiment poised parallel to the axis of the bar 
magnet. 

117. The Poles Misnamed. — Gilbert called attention to a fact 
following directly from his discovery, that is, that the pole of the 
needle which is attracted by the earth's north magnetic pole (and 
which we have called its north pole) should strictly be called its 
south pole. Subsequent writers in view of this have sought to 
avoid confusion by using the terms "north-seeking pole" and 
"south-seeking pole," but it is thought that the shorter expres- 
sions are sufficiently sanctioned by custom and that no ambiguity 
will arise if in the following pages the pole of the needle which 
points north be designated its north pole, the other, its south 
pole. 

118. Magnetization by Induction. — A soft iron nail touched 
to a bar magnet will cling to it. If a second nail be now touched, 



MAGNETISM. 



91 




not to the magnet but to the first nail (Fig. 54), it will cling to this 
nail and even a third nail may be attached to the second and so on. 
If while thus dangling the several 
nails be tested, each will be found 
to possess polarity, the upper ends 
being of opposite polarity to that 
end of the magnet to which they 
are clinging, the lower ends being 
of the same polarity. If the mag- 
net be removed the chain of nails 
will fall apart. The magnet there- Flg - 54 - 

fore influences the nails so that for the time being they them- 
selves are magnets. This is the explanation of the chains of filings 
referred to in Par. 112. The phenomenon is called magnetization 
by induction. 

119. Induction Takes Place Through Space. — Actual contact 
is not necessary for induction. A piece of iron or steel placed 
anywhere in the vicinity of a magnet becomes temporarily a 
magnet. This fact is clearly shown by the following experiment. 
A soft iron bar AB (Fig. 55) free from magnetism is arranged 




Fig. 55. 



upon a convenient support. Near the end B but not so near as 
to be attracted into contact is placed a needle. If the north 
pole AT" of a bar magnet be approached to the end A of the iron 
bar, but not actually touching the same, the north pole of the 
needle will be repelled from B. The bar AB becomes a magnet 
by induction, the end B becoming the north pole and repelling 
the north pole of the needle. To show that the repulsion of the 
needle is not due to the direct action of the bar magnet, if AB be 
removed the effect of the bar magnet upon the needle is almost 
negligible. 



92 ELEMENTS OF ELECTRICITY. 

120. Magnetic Attraction Explained. — The foregoing enables 
us to explain magnetic attraction. A piece of iron or steel near a 
magnet becomes a magnet by induction. The near end of the 
piece is of opposite polarity and hence attracted; the farther end 
is repelled but the attraction is stronger than the repulsion (mag- 
netic attraction and repulsion will shortly be shown to follow the 
law of inverse squares) and the piece, if free to do so, will move 
bodily up to the magnet. As in the case of electric charges, in- 
duction precedes attraction. 

121. Other Magnetic Substances. — We have heretofore men- 
tioned only iron, steel and the lodestone as being magnetic sub- 
stances. Two other metals, nickel and cobalt, are noticeably 
magnetic, though much less so than the above mentioned, and many 
substances are feebly so, so feebly however that the property can 
be detected only by the most delicate apparatus and for practical 
purposes may be neglected. Among these substances are some of 
the salts of iron, and oxygen, especially when liquefied. 

Gilbert carefully distinguished between magnets and magnetic 
substances. A magnet exerts its attraction at certain portions 
only, has polarity and its poles will repel similar poles of a second 
magnet. A magnetic substance, such as soft iron, has no polarity, 
attracts either pole of a magnet at any portion of its surface and 
does not attract other magnetic substances. 

122. Diamagnetism. — It has long been known that some sub- 
stances, notably bismuth and antimony, are repelled from the 
poles of a magnet, the bodies placing themselves so that their 
longer axis is at right angles to the magnet. Explanation of this 
phenomenon can not be given until the subject of electro-magnetics 
is reached (Par. 402). The repulsion is very feeble and delicate 
instruments are required to detect it. Faraday investigated the 
magnetic properties of many bodies and those which are attracted 
he called paramagnetics; those which are repelled, diamagnetics. 
The majority of liquids, except those containing in solution the 
salts of iron, are feebly diamagnetic. The subject is of theoretical 
interest only. 



MAGNETISM. 



98 



CHAPTER 13. 



MEASUREMENT OF MAGNETIC FORCES. 



123. Coulomb's First Law. — The first law of magnetic force 
has already been given (Par. 115) and is that like poles repel and 
unlike poles attract one another. The second law deals with the 
variation of this force of attraction or repulsion. Before develop- 
ing it, we must get some preliminary notion of what is meant by 
the strength of magnets. 

124. Lifting Power of Magnets.— At first sight it might seem 
that a simple way to determine and compare the strength of mag- 
nets would be to ascertain the weight which they could support. 
Various pieces of apparatus have been devised for this purpose. 
For example (Fig. 56) the magnet is held vertically in a frame 
and supports by its attraction an iron piece or armature A. 
Attached to this armature is a hook from ^^ 
which hangs a receptacle into which fine 
sand is slowly poured. When the accumu- 
lated weight reaches a certain point the 
armature is torn away and with the recep- 
tacle drops to a table placed just beneath 
to receive it. The total weight supported n\ * 
by the magnet is then determined by \a\ 
weighing. \\ 

When, however, the conditions of this \)( 

experiment are varied, it will be seen that 
these results are of but little value. The 
following will make this clear. 

(a) If one end of a bar magnet be 
rounded and the other be squared, the 
rounded end will lift a greater weight than 
the squared end, and this although it can Fi l 
be shown that the two ends are of equal magnetism, 
lifted therefore varies with the shape of the pole. 

(b) If the magnet be bent into a horseshoe shape so that both 
poles concur in the lifting, instead of the weight being just twice 




56. 



The weight 



94 ELEMENTS OF ELECTRICITY. 

what it was before for a single pole, it may be three or even four 
times greater. The weight lifted therefore varies with the shape 
of the magnet. 

(c) If the weight be applied very gradually the magnet will 
support more than it would if it were applied suddenly. If a 
magnet be loaded to nearly the maximum point and the load be 
left in position for a day, the weight may then be gradually in- 
creased until it considerably exceeds the original maximum. Once, 
however, that the armature is torn away, the lifting power of the 
magnet drops back to what it was formerly. 

(d) Within certain limits, the larger the armature the greater 
the weight lifted. 

(e) The weight lifted varies with the character of the iron or 
steel of which the armature is composed. 

(f) Retaining the same weight and composition, a greater 
weight will be lifted if the armature be of a compact shape, such 
as a cube, than if it be a flat disc. The weight lifted therefore 
varies with the size and shape of the armature. 

In the last four cases above we see that although the magnet 
itself does not vary, the weight lifted fluctuates through a wide 
range. We can not say which of these weights should be taken 
to measure the strength of the magnet nor is it practicable to give 
mathematical expression to the heterogeneous conditions enu- 
merated and deduce formulas from which this strength might 
be calculated. What we have done therefore is not to measure 
the strength of the magnet but its lifting power under certain given 
conditions. 

A small bar magnet should lift from 15 to 25 times its own 
weight. In the Paris Exhibition of 1882 there was shown a magnet 
which supported 76 times its own weight. Thompson states that 
the lifting power of a good steel magnet may amount to 40 pounds 
per square inch of pole surface. Electro-magnets, to be described 
later, are much more powerful, the lifting power reaching 200 
pounds per square inch. 

125. Strength of Magnets. — If we examine the force with 
which one magnet attracts or repels another, the two being at 
some distance apart, we find that it is not affected by shape of 
poles or length of exposure to each other's influence, etc., but is 
to a great extent independent of the varying conditions mentioned 
in the preceding paragraph. The force with which magnetic poles 



MAGNETISM. 



95 



interact is therefore selected as the measure of their strength. We 
are thus naturally led to enquire what is precisely a magnetic pole 
and how is the force between two poles measured. 

126. Magnetic Pole Defined. — In the preceding pages we have 
used the word pole to designate rather vaguely the terminal por- 
tions of a magnet, the regions in which the magnetic force is most 
marked. In mathematical discussions it is desirable to treat a 
pole as if it were a focus or the point of application of the resultant 
of the magnetic forces at that particular end of the magnet. This 
point may be approximately located as follows. In a bar magnet 
the magnetic forces are symmetrically distributed around its axis 
and the pole must consequently lie upon this axis. In Fig. 57 let 
MN represent one-half of the bar magnet which is supported 




Fig. 57. 



horizontally. With a pencil mark off this half in equal divisions. 
Cut a small soft iron wire into a number of short pieces of equal 
length (and hence of equal weight). Apply the end of one of these 
pieces to one of the divisions of the bar and then other pieces to 
the first piece until the accumulated cluster drops off of its own 
weight. Note the particular division and the corresponding- 
number of pieces. Repeat this for each of the divisions, then 
construct a curve MBN in which the divisions are the abscissa? 
and the ordinates are laid off to a scale to represent the number of 
pieces of wire supported. The pole is on the axis of the magnet 
and approximately opposite the center of gravity of the tri- 
angular figure MBN. 



96 ELEMENTS OF ELECTRICITY. 

In short thick magnets the poles are distributed over a con- 
siderable area but for long slender bars they approach the ends 
and approximate the hypothetical point or focus. According to 
Fleming, the poles of a bar magnet are about one-twelfth of its 
length from the ends. For shorter and thicker bars this distance 
may amount to one-sixth or even one-fifth. 

It will be shown later (Par. 146) that for certain magnetic 
measurements the exact location of the pole is immaterial. 

Although it is impossible to get a magnetic pole unaccompanied 
by an equal and opposite pole, yet in a long slender magnet the 
poles are so far apart that in many experiments the effect of the 
more distant one may be neglected and the results are as if we 
were dealing with a single or "free" pole. 

127. Measurement of Magnetic Forces. — The measurement of 
magnetic forces is not entirely a simple .matter. Two magnets, 
A and B, exposed to each other's influence are each acted upon by 
four forces. The north pole of A is repelled by the north pole of 
B and attracted by its south pole; the south pole of A is repelled 
by the south pole of B and attracted by its north pole. In addi- 
tion, each magnet is acted upon by the earth's magnetic poles so 
that each is subject to eight forces. 

In most cases the forces are comparatively feeble. They must 
therefore be measured by comparing them with, or by balancing 
them against, other forces, likewise feeble, whose variation follows 
some readily determined law. The forces used for comparison 
are — 

(a) A known magnetic force, usually that of the earth. There 
are two methods of comparison, both of which will shortly be 
described (Pars. 129, 146). 

(b) The torsion of a suspending thread, as in Coulomb's torsion 
balance, already described (Par. 52). The law in this case is that 
the force varies directly as the angle through which the thread is 
twisted. 

(c) The force of gravity applied through a bifilar suspension. 
A magnet is suspended in a horizontal position by two parallel 
threads. If it be deflected the threads must be twisted from a 
vertical to an oblique position and the magnet must therefore be 
raised. The law in this case is that the force varies directly as the 
sine of the angle through which the magnet is twisted. 



MAGNETISM. 97 

128. Coulomb's Second Law. — The second law of magnetic 
force comprises two statements. First, the force exerted between 
two magnetic poles varies directly with the product of their 
strengths, and second, this force varies inversely as the square of 
the distance separating them. The distance between the poles is 
supposed to be so great that they may be regarded as points. 

The first of these statements hardly requires proof since it 
follows at once from the fact that the action between poles is 
mutual and that if we double or treble the strength of either one 
we double or treble the force exerted between them. Its truth 
may easily be shown experimentally. The second statement 
is proved experimentally by one of the methods now to be 
described. 

129. Method by Oscillations. — From mechanics, the time of 
oscillation of a simple pendulum, its angular displacement being 
small, is given by the equation 

in which I is the length of 
the pendulum and g is the acceleration due to gravity. The force 
acting upon the pendulum is mg, m being its mass. The above 
expression may be written 



y ma V 



ml 



mg V force 

whence 

Force = ^L ■ = constant X t™ 
1 - l z 

But y is the number of oscillations n in a unit of time, hence 

Force = constant Xn 2 , 

or the force producing 
pendular vibrations is proportional to the square of the number 
of vibrations executed in a unit of time. Any convenient inter- 
val of time may be taken as the unit. 

If a magnetic needle AB (Fig. 58), whose position of rest is 
along the magnetic meridian NS, be pushed aside through an 
angle 8 and then released, it will be acted upon by forces tending 



98 ELEMENTS OF ELECTRICITY. 

to return it to its primary position but in swinging back it will 
acquire a momentum which will carry it very nearly an equal 
N x> angular distance beyond NS and will then swing 
/a in the opposite direction and so on, that is, the 
••' ! needle will act as a double pendulum in a hori- 
\ !y zontal plane and if 5 be small will execute oscil- 
/yf\ lations whose period is practically constant. The 
/ forces which tend to restore the needle to its posi- 
tion in the meridian are due to the interaction of 
the poles of the magnet and those of the earth. 
The earth being a sphere and its poles being 
located beneath its surface, their action lines are 
oblique to the plane of oscillation of the needle 
and only the horizontal component of the forces 
along these lines affects the oscillations. This 
5 horizontal component of the earth's magnetism 

Fig. 58. j s USU ally designated by the letter H. Within the 

limits of space covered by the average experiment H is constant. 
If the strength of the poles of the needle be represented by ra, the 
force acting upon each pole will be m H, represented in Fig. 58 by 
AD and BC and, from what we have seen above, this force is pro- 
portional to the square of the number of oscillations executed by 
the needle in a given time. How this principle may be utilized in 
measurements will be shown in Par. 131. 

130. Magnetic Moment. — The active components of the forces 
AD and BC (Fig. 58) are AE and BF, each of which is equal 
to m.H.sm.8. These constitute a couple whose moment is 
m.H. sin 8.1, I being the distance between the two poles. The 
product ml is called the magnetic moment of the needle and in 
formulas is represented by M. Although the exact position of 
the poles, and consequently the distance I, is most often unknown, 
M itself may be determined by experiment and is used in certain 
magnetic measurements to be described later (Pars. 148, 149, 150). 

131. Experimental Proof of Law of Inverse Squares. — In 

Fig. 59, A is a very small magnet, less than half an inch in length, 
suspended in a paper stirrup by a single fibre of unspun silk and 
at rest in the magnetic meridian. The resistance of the silk fibre 
being very slight, if the magnet be started in oscillation it will 
continue so for from five to ten minutes. It is given a slight im- 



MAGNETISM. 99 

pulse and the number of oscillations executed in a given interval, 
say one minute, is counted. Suppose this number to be 10. A 
slender bar magnet B is now placed in the same meridian, its axis 
in the prolongation of the axis of A. (This experiment may also 
be performed with the magnet B in a vertical position, its pole 
being in the meridian and horizontal plane of A.) B must be 
placed at such distance from A that for small angular deviations 
of A the action lines of B are sensibly parallel. This is also one of 
the reasons for keeping A very small, the other being that if A be 
small its poles are more nearly the same distance from the pole of 
B. A is again set in motion and if the poles of the bar magnet 



5^^ Fig. 59. 

coincide in direction with those of A, the oscillations will be more 
rapid. Suppose that now 12 are executed in one minute. The 
force due to the horizontal component of the earth's magnetism 
is to the combined force of this component and that of the pole of 
B as 100 is to 144. Let B now be pushed up towards A until the 
distance between its pole and that of A has been halved. A set in 
motion will now be found to execute about 16.5 oscillations per 
minute. The total force upon A in the first place is to that in the 
second as (12) 2 is to (16.5) 2 or as 144 is to 272. The force due to B 
alone is as (144-100) is to (272-100) or as 44 is to 172, which is 
very nearly as 1 is to 4. In other words, as the distance is halved 
the force is quadrupled, which is in accordance with the law of 
inverse squares. 

In the above proof the distance between the poles of the two 
magnets must be known and as the exact position of the poles 
themselves is not precise, their distance apart is apparently un- 
certain; however, this distance may be assumed as nearly as pos- 
sible and one or two trial experiments thereafter will show what 
the correct distance should be. 

132. Proof of Law of Inverse Squares by Coulomb's Balance. 

— Coulomb also proved this law by means of the balance which 
bears his name. A description of the actual experiment would be 



100 ELEMENTS OF ELECTRICITY. 

somewhat long and it will suffice to say that in the apparatus as 
represented in Fig. 22, a slender bar magnet took the place of the 
shellac needle G and a second one took that of K H. The instru- 
ment was set up so that with no torsion on the suspending fibre, 
Hie horizontal needle and the opening K in the glass cover lay in 
the same magnetic meridian. The experiment was then conducted 
as explained in Par. 52, due allowance being made for the effect of 
the earth's magnetism. 

133. Unit Magnetic Pole. — Magnetic poles differ in strength. 
We may consider that there is more magnetism concentrated at 
the stronger pole or may assume that there are magnetic poles of 
unit strength and that a greater number of these are gathered at 
the stronger pole. A definite conception of a unit pole may be 
obtained from the following. Coulomb's second law may be 
expressed thus, 

- _ ra X ra' 
; ~ d 2 ' 

in which, since we are 
using the C. G. S. system, / is the force in dynes between the poles, 
ra and ra' the strength of the respective poles and d their distance 
apart in centimeters. If the poles be of equal strength this 
becomes 

- _ ra 2 
J ~~o¥ 

and if we make the further assumption that the poles be one 
centimeter apart , the expression reduces to 

/ = ra 2 



Now, if the pole strength ra be large, the force / will be large; 
if it be small, this force will be small. By varying ra we could 
finally obtain such a value that / would become one dyne. At 
this instant, ra = 1, and this unit we call the unit magnetic pole 
and define it as that pole which when placed at a distance of one 
centimeter from a similar and equal pole repels it with a force of 
one dyne. 



MAGNETISM. 101 



CHAPTER 14. 

THE MAGNETIC FIELD. 

134. Magnetic Field. — In the space around a magnet all poles 
experience forces of attraction and of repulsion and this space is 
called the field of the magnet. As we recede from the magnet 
these forces diminish in accordance with the law of inverse squares 
and, to fix its limits more definitely, we define a magnetic field as 
that space surrounding a magnet in which magnetic force due to 
this magnet is perceptible. 

135. Direction of Magnetic Field. — As an aid to the conception 
of a magnetic field we may resort to the same analogy as in the case 
of the electric field (Par. 58) and compare it to a current of water. 
In a magnetic field there is no matter in actual movement but 
there is in a certain sense a flow of force and magnetic poles, placed 
in the field, are swept along just as light objects are carried by a 
stream. Since free north poles would be carried along in one 
direction and free south poles in the opposite direction we by 
convention define the positive direction of a magnetic field as that 
direction in which a free north pole would move. 

136. Intensity of Magnetic Field. — Just as we might measure 
the strength of a current by the force with which it pushes a board 
of unit area placed in it, so we agree to measure the intensity of a 
magnetic field by the force with which it acts upon a unit pole 
placed in it and we define a unit magnetic field as that field which 
acts with a force of one dyne upon a unit pole placed in it. If we 
say that a magnetic field has a strength of three, we mean that it 
will act with a force of three dynes upon a unit pole placed in it. 
If the strength of the field be H and that of the pole be m, the 
force with which the field acts upon the pole is Hm dynes. From 
the foregoing and from Par. 128 it follows that the field at a dis- 
tance d from a pole of strength m is m/d 2 . 

137. Magnetic Lines of Force. — In Fig. 60 let P be a point in 
the field of the bar magnet NS and for simplicity of construction 
suppose that at this point the distance SP is twice the distance 



102 



ELEMENTS OF ELECTRICITY. 



NP. Suppose a free north pole to be placed at the point P. It 
will be repelled from N along NP and attracted towards S along 
PS. In the case assumed the distance NP being only one-half of 
PS, by the law of inverse squares the repulsion along NP is four 



\ 




Mf 



*>1 



P 



H 



R' 



/ 



/ 



Fig. 60. 



\ 



times as great as the attraction along PS. Lay off PB any con- 
venient distance and PA four times as great and complete the 
parallelogram. PR is the resultant at the point P of the magnetic 
forces of the two poles N and S or, in other words, the free north 
pole at P will be urged along the resultant PR with a force pro- 
portional to PR. 

Suppose this free north pole to move along PR a very small 
distance. In doing so it will move away from N more rapidly 
than it does from S. This will cause the repulsion from AT" to grow 
weaker and the attraction to S to grow relatively stronger and the 
path of the pole will bend around towards S. In its successive 
positions therefore, the pole will follow a curve which at every 
point indicates by its direction the direction of the resultant of 
the magnetic forces at that point. This curve is called a magnetic 
line of force. 

If instead of a free north pole a free south pole had been placed 
at P, it would have been urged with an exactly equal force in an 
exactly opposite direction PR', and in its path would have traced 
out the same curved line but in a reverse direction. By convention 
(Par. 135) we define the positive direction of a magnetic line of 
force as that direction in which a free north pole would move. In 



MAGNETISM. 



103 



our diagrams the positive direction of these lines is always in- 
dicated by an arrowhead placed upon the lines. 

138. Mapping Lines of Force. — If at any point P (Fig. 60) 
there be placed a very small magnetic needle, its north pole would 
be urged in the direction PR, its south pole in the direction PR', 
and the needle will take up a position approximately tangent to 
the line of force at the point P. If a sufficient number of these 
little needles be placed one after the other, as shown in Fig. 60, 




Fig. 61. 

the successive tangents which they indicate will serve as an enve- 
lope and will mark out the line of force, approximating more and 
more closely to it as their length is decreased and number increased. 
Finally, if the entire space about the magnet were strewn closely 
with the little needles a number of lines of force would be 
traced. 

This condition may be realized practically as follows. A sheet 
of glass, of stiff paper or of any non-magnetic body is placed upon 
a magnet and is then sprinkled with fine iron filings. From what 
we have already seen (Par. 120) each individual filing becomes for 
the time being a magnet, but these little magnets are not free to 



104 ELEMENTS OF ELECTRICITY. 

move since their weight holds them with friction against the sur- 
face over which they are sprinkled. If the sheet be given a gentle 
tap the filings are jarred and for a minute interval of time are 
bounced up into the air. Being now freed from the friction which 
held them in place, they move under the influence of the magnetic 
forces and after a few repetitions of the jarring they gather along 
well marked lines as shown in Fig. 61. 

139. Permanent Record of Magnetic Figures. — Several ways 
have been described by which these magnetic figures, or curves 
traced by the filings, may be recorded permanently. The following 
is simple and convenient. Upon a soft pine board about a foot 
square the magnet is placed and its outline is traced with a pencil. 
With a chisel this outline is then hollowed out until when in posi- 
tion the upper surface of the magnet is on a level with that of the 
board. The board is then taken into a subdued light and there is 
pinned upon it, prepared surface up, a sheet of blue-print paper 
about 8x10 inches. Iron filings are then sprinkled over this paper 
and the board is tapped on the under side until the magnetic 
figures come out as desired. Better results are obtained if before 
using the filings they are passed through two sieves, one to separate 
the dust-like particles and the other those of too large size. The 
board with the filings in position is then exposed in "a strong 
sunlight for from three to five minutes, the rays falling as 
nearly perpendicular to the paper as possible. It is then carried 
back to the subdued light, the filings poured off and the paper 
thoroughly washed in clear water. The resulting blue-print is 
then dried. 

140. Use of Magnetic Figures. — These magnetic figures are of 
assistance in the study of magnetic fields and often enable us to 
grasp at a glance conditions which might otherwise require con- 
siderable mathematical analysis to develop. For example, they 
show in a striking manner how the field between two mutually 
attracting poles differs from that between two that mutually 
repel. Fig. 62 represents the field between two dissimilar poles. 
In this the lines of force are seen to pass from one to the other as 
if pulling them together. At the same time these lines are bowed 
out revealing the existence of the crosswise pressure causing them 
to separate. Fig. 63 shows the field between two similar poles and 
it does not require a great stretch of the imagination to conceive 



MAGNETISM. 



105 



of the lines of force as hands placed palm against palm and pushing 
each other back. Further examples of the use of these figures will 
be met in subsequent pages. 




Fig. 62. 




Fig. 63. 

141. Compounding Magnetic Fields. — The magnetic fields 
hitherto considered are those surrounding a single pole or pair of 
poles and are symmetrical with respect to the single pole or to the 
line joining the two poles. Should these fields be intersected by 
another, the resultant field would be obtained by compounding 



106 



ELEMENTS OF ELECTRICITY. 



the two and would in general be unsymmetrical. The earth's 
field most often produces distortion in others but its strength 
being comparatively feeble, the distortion is not revealed in the 
magnetic figures produced with filings. If, however, the field be 
mapped as follows the effect of the earth's field becomes evident. 
Place a bar magnet in the center of a sheet of paper and then in 
contact with the magnet place one of the little compass needles one 
centimeter in length and mounted in a glass-covered brass case. 
With a pencil make a dot at the far end of the needle, then shift 
the compass until the near end of the needle is over this dot and 




Fig. 64. 



again make a dot at the new position of the far end of the needle 
and so on to the limits of the paper. Connect these dots by a 
continuous curve. Start with the compass at some other point 
along the magnet and make a second chain of dots and so on until 
the whole space about the magnet has been marked off. Figs. 64 
and 65 represent fields traced in this way, Fig. 64 with the north 
pole of the bar magnet pointing north, Fig. 65 with the north pole 
pointing south. In each case immediately around the magnet 
the strength of its field overpowers that of the earth but the 
strength of the magnet's field falls off rapidly as the distance from 
it increases while the earth's field is constant over a considerable 



MAGNETISM. 



107 



area and at a distance from the magnet the earth's field has the 
ascendancy. At the spots marked P these two forces neutralize 
each other and the needle will vacillate and come to rest in any 
position. These two figures, though different, are both symmet- 
rical since the bar magnet was designedly placed in a north and 
south position. Should it be placed in any oblique position the 
symmetry will be destroyed. 




Fig. 65. 

142. Properties of Magnetic Lines of Force. — In some of 
their properties magnetic lines of force are similar to electric lines 
of force but in others they differ widely. They agree with electric 
lines of force in having a tension along their length, or a tendency 
to shorten, and also a pressure at right angles. They also never 
intersect. They differ from electric lines of force in that they are 
closed curves, that they penetrate all substances whether con- 
ductors or not and that they do not necessarily, or even generally, 
leave or enter a surface at right angles. Being a closed curve, a 
complete magnetic line of force lies partly in the magnet and 
partly in the surrounding medium. While the majority of these 
lines emerge near the poles, many, as shown in Figs. 61 and 66, 
emerge along the sides of the magnet. The lines within the magnet 



108 ELEMENTS OF ELECTRICITY. 

are designated collectively as the magnetic flux ana this flux is 
evidently a maximum at the mid-section of the magnet. This 
is sometimes otherwise expressed by saying that the intrinsic 
magnetism is a maximum at this mid -section. The intrinsic 
magnetism is of no effect on outside bodies. Magnetic effects 
of attraction and repulsion are produced only by those lines of 
force which emerge from the magnet. This is called the free 
magnetism and is greatest in the neighborhood of the poles. 




Fig. 66. 

It must be noted here that that portion of these lines which lies 
within the magnet does not conform to the definition of a line of 
force as given in Par. 137, for which reason these internal lines 
have been variously designated as lines of magnetization, lines 
of magnetic induction, etc. An internal line of magnetization is, 
however, always the continuation of an external line of force and 
the above distinction, although academically correct, is without 
practical importance. This fact will be brought out more clearly 
in the subject of electro-magnetics. 

That portion of a magnetic body from which lines of force 
emerge is always a north pole and that portion of such body into 
which they enter is always a south pole. To this rule there is but 
one exception. The lines of force of the earth enter at the north 
magnetic pole and come out at the south magnetic pole. The 
reason for this exception has already been given (Par. 117). 

143. Magnetic Lines Pass Preferably Through Magnetic 
Substances. — If in the space between the two dissimilar poles in 
Fig. 62 there be inserted a soft iron block and a magnetic figure 
be then taken, the lines of force which in Fig. 62 curved out widely 
will now be seen to have drawn in, as shown in Fig. 67, and pass 
through the iron block instead of through the air. A simple ex- 
planation is that the iron block has become a magnet by induction 
and the lines of force converge to the nearest poles, but it is some- 
times conveniently explained by the statement that magnetic 



MAGNETISM. 



109 



lines of force travel by preference through magnetic bodies and 
will avail themselves of such a path whenever the opportunity 
offers. This principle affords an explanation of certain phenomena 
and is of considerable practical importance. 




Fig. 67. 

It has already been noted (Par. 112) that filings cling to the 
edges of a magnet rather than to the flat surfaces. This fact is 
also clearly shown in Figs. 61, 62 and 63. In Fig. 68, a and b 
represent end views of a bar magnet. If the lines of force radiated 
equally from the internal pole they would emerge as shown in a 
and there would be more filings just on top of the magnet than 
elsewhere since this point is nearest to the pole and consequently 



^txte^H'" " 



-HV 



Fig. 68. 



at this point the attraction would be strongest. But since the 
lines prefer to travel as far as possible through the steel, their 
actual path is as represented in b and the filings are thickest 
where the lines of force are thickest, that is, along the edges. 

An essential part of dynamos and motors consists in its simplest 
form of two powerful magnetic poles embracing between them a 
cylindrical opening. It is highly important that there should be a 



110 



ELEMENTS, OF ELECTRICITY. 



uniform field along the faces of these magnets but owing to the 
principle above, the lines of force, as shown in Fig. 69 a, crowd 
across at the top and bottom and leave the central portion of the 
opening thin. If, however, there be inserted in this space a soft 




Fig. 69. 



iron cylinder, the lines will pass through this cylinder and, as 
shown in b, will produce along the pole faces a dense and uniform 
field. 

If a magnet NS (Fig. 70) produces a deflection in a needle A, 
the needle can be screened from this effect by interposing between 



B 



Fig. 70. 

it and the magnet a comparatively thick iron plate B. The lines 
of force from N, which formerly reached A, now travel through 
B, as shown in the figure, and thence back to S. If A be placed 
inside of an iron cylinder it may be entirely screened from outside 
magnetic influences. 



MAGNETISM. 



Ill 




If a pivoted iron bar AB (Fig. 71) be placed diagonally across 
a magnetic field NS it will swing so as to place itself parallel to 
the field. We may explain this motion as 
follows. The lines of force of the field, from 
what we have just seen, turn to one side and, 
as shown in the figure, run lengthwise 
through the bar. The tension along these 
lines produces a couple on AB which pulls 
it around to parallelism with NS. The law 
under which this movement takes place is 
that a magnetic body placed in a magnetic 
field tends to move so that its longest axis 
coincides in direction with the lines of force 
of the field. 

144. Law of Maximum Flux. — In Fig. 72, 
A is a piece of soft iron in a weak field to 
one side of the strong field B. The lines of force of the strong 
field move out, as shown in the figure, so as to pass through 

A and if A be free to move it will be 
drawn over into the denser field at B. 
If A be a magnet placed obliquely to B 
it will be both drawn over into B and 
turned so that its own lines of force will 
be parallel to and of the same direction 
as those of B. It will therefore embrace 
in lengthwise direction both its own 
lines of force and those of the field B, or : 
in general, a magnetic body placed in a 
magnetic field tends to move so as to 
embrace in one direction the maximum 
number of lines of force. This is but a 
lg * "" particular case of Maxwell's Law, a prin- 

ciple of great importance which will be discussed later (Par. 371). 

145. Graphic Representation of Intensity of Magnetic Field. — 

For the same reasons as given in Par. 61, it has been agreed to 
represent graphically the intensity of a magnetic field by the 
number of lines of force per square centimeter taken perpendicular 
to these lines. From this standpoint, a unit magnetic field is 
defined as that field which contains one line of force per square 






\ \ 
i \ 



i 
i , 



1 1 1 
1 1 1 
1 1 1 




1 

I 

1 






\ \\ 


I 




K X ^ N 


1 1 




^ N v^ v 


1 /' 




V^%\s 


1 / 


/ 


\ m\ 


I / 


i 


1 / 


i 


\ 


i%V 


!/ 




i 


I 


1 1 1 


1 1 




' 


B i <- 

i 


1 1 j 


ji 


A 


i 
i 
\ 




i\ 


\ 




i\ 


\ 

\ 

\ 








/''/''' 


■ \ 


i 
i 


' 1 ' 




i 

i 

i 
i 




i 
i 
i 

i 



112 



ELEMENTS OF ELECTRICITY. 



centimeter of cross-section. A similar course of reasoning to that 
given in Par. 63 will lead to the conclusion that there radiate 
from a unit pole 4 tt lines of force. 

146. Comparison of Magnetic Fields. Tangent Law. — There 
are a number of ways in which magnetic fields may be compared 
by means of the deflection which they produce in a magnetic needle. 
If a needle which is poised in the meridian be exposed to such a 
field at right angles to the meridian, the needle will be deflected 
through a certain angle. The field draws it to one side with a 
decreasing moment; the horizontal component of the earth's mag- 
netism pulls it back to the meridian with an increasing moment. 
A position of equilibrium is finally reached and the angle of 
deflection may be read from a scale placed beneath the needle. 

In general, in instruments which operate thus by a needle 
moving over a scale, the force which pulls the needle away from 
its zero position is called the deflecting force; the force which tends 
to restore it to the zero position is called the controlling force. 

In the following method it is assumed that the action lines of 
the magnetic force upon the poles of the needle are parallel and 
that within the limits of the space over which the needle swings the 
force is constant. In order to realize this condition as nearly as 
possible the needle is made very small. If the scale of degrees 
varied with the size of the needle it would become too small to be 
read with much accuracy, therefore an auxiliary pointer of alum- 
inum or of some other light substance 
is fastened to the needle and a larger 
scale may then be used. 

In Fig. 73 let AB he a magnetic 
needle of pole strength m, deflected 
from the meridian NS through an 
angle 5 by a magnetic field H f act- 
ing at right angles to the meridian. 
At the pole A the controlling force 
is mH, represented by AC. The 
deflecting force is mH', represented 
by AD. An exactly similar set of 
forces act upon the pole B but to 
consider them would simply be to 
repeat what we shall prove for the set at A. The controlling 
force may be divided into two components, one, AF, in the 




MAGNETISM. 113 

direction of the axis of the needle and of no effect so far as 
rotation is concerned; the other, AE, perpendicular to the needle 
and active in restoring it to the meridian. From Fig. 73, 
AE = AC. sin 5 = mH. sin 5 

Similarly, the deflecting force may be divided into two com- 
ponents, one in the direction AF, the other AG, which = AD . cos 5 
= mH f . cos 8 and which is active in deflecting the needle from 
the meridian. When the needle comes to rest these two active 
components, AE and AG, are equal, hence 
mH' .cos8 = mH. sinS 

whence H' = H • ^~ = H. tan<5 

cos 5 

or, the magnetic 
field which acting at right angles to the meridian produces in a 
magnetic needle a deflection 8, is equal to the horizontal component 
of the earth's magnetism at that point multiplied by the tangent 
of the angle of deflection. 

It follows direct from the foregoing that different magnetic 
fields acting at right angles with the meridian will deflect a 
needle through angles whose tangents are proportional to the 
respective fields. This is known as the Tangent Law and is of 
extreme importance since, as will be shown later (Par. 374), it 
affords a means for the absolute measurement of the electric 
current. 

It will be noted that the deflection produced is independent of 
the strength and of the length of the needle, or rather of the dis- 
tance between the poles. Hence, as was stated in Par. 126, the 
exact location of the poles is immaterial. If, however, the con- 
trolling force be non-magnetic these factors are of importance. 

147. The Sine Law. — Should the deflecting field make a con- 
stant angle with the needle instead of with the meridian, a different 
state of affairs would result. Whatever the constant angle may be, 
we can always divide the force into two components, one of which 
is perpendicular to the needle and is the effective one in producing 
deflection. We may therefore in Fig. 73 consider AG as repre- 
senting the deflecting force mH'. When equilibrium is reached 
AG = AE, or 

mH' =mH . sin 8, or H' = H .sm 8 

whence, magnetic fields acting at a constant angle with the needle 



114 ELEMENTS OF ELECTRICITY. 

are to each other as the sines of the respective angles of deflection. 
This is known as the Sine Law and is the principle of one class of 
galvanometers (Par. 376). 

148. Determination of the Strength of a Magnetic Field. — In 

Pars. 129, 146 and 147, principles have been given which enable 
us to compare magnetic fields among themselves, that is, to deter- 
mine how many times stronger or weaker one field is than another, 
but these do not enable us to make any absolute measurement. 
The following method of determination of the absolute strength 
of a magnetic field is due to Gauss. 

In Par. 129 we saw that the time of oscillation of a simple 
pendulum is given by the expression 



V force 

Multiplying the expression under the radical sign by I above 
and below, it becomes 

m.P 
I X force 
In mechanics, the sum of the product of the mass of each particle 
of a rotating body into the square of the distance of the particle 
from the axis of rotation is called the moment of inertia of the body. 
In the above expression m is the concentrated mass of the pendu- 
lum and I is its distance from the point of suspension, therefore, 
m .I 2 is the moment of inertia of the pendulum. Representing this 
by K, the above becomes 

K 
I X force 
In the case of a needle in a magnetic field, the force is m . H, m 
now representing the strength of the pole of the needle, and the 
above may be written 

K 
l.m.H 
But (Par. 130) I. mis the magnetic moment of the needle, hence 
the expression becomes 

K 



M.H 

The expression for the time of oscillation may therefore be 
written 



t = 2t \ith 



MAGNETISM. 115 

In this, T can be determined by observation and K by calcula- 
tion or by experiment.* We therefore have an equation involving 
two unknown quantities M and H, one of which, H, we wish to 
determine. If we can obtain another expression involving these 
same two quantities, we may by combination determine H. The 
obtaining of this second expression is explained in the two follow- 
ing paragraphs. 

149. Turning Moment of One Magnet upon Another. — Let 

ns (Fig. 74) be a small magnetic needle, its center lying on the 
prolongation of the axis of the magnet NS and its length perpen- 
dicular to this prolongation. Let m' be the strength of the poles 



A„ n 



A 



Fig. 74. 







S 



of ns and let m be that of the poles of NS. Let the distance 
between the poles of ns be 21 and that between the poles of NS 
be2L. Let OC = D and Nn=d. From the figure d = Vp+(D- L) 2 . 
The repulsion between N and n is m . m' Id? and the moment of this 
force upon ns is 

^XOA 

The triangles NOn and OnA are similar since they are both 
right angled and have a common angle NnO, hence 

OA : On = NO : Nn 

Hence OA = °\>5 N0 

Nn 

l(D - L ) 
d 

l(D-L) 

VP + (D - Lf 

* The moment of inertia of a bar magnet is 

T . ( (length) 2 + (breadth) -\ vy 

K = ( - — ' j X mass 

that of a cylindrical magnet is 

K= pj^ 2 + (Ef^:) Xmass 



116 ELEMENTS OF ELECTRICITY. 

Hence the above moment is 

m.m'.l (D — L) 
[I 2 + (D - L) 2 ]i 
The moment of N on s is the same and the total moment due 
to Afis 

2m.m'.l(D - L) 

[I 2 +(D- L) 2 ]* 

The moment due to S is found in the same manner and may be 

obtained direct from the preceding expression by substituting 

D + L for D — L. Since it acts in the opposite direction to that 

due to N, the resultant component is 

2.m.m'.l(D - L) _ 2.m.m f .1 (D + L) 
[P + (D - L) 2 f [I 2 + (D + L) 2 ]i 

If ns be very small, I 2 can be neglected in comparison to (D — L) 2 , 
and consequently also in comparison to (D + L) 2 , and the above 
expression can be written 

I I 



2.m.m' .1 



(D - L) 2 (D + L) 2 
DL 



or S.m.m'.l^ D2 _ U)2 

Finally, if the distance between the two magnets be so great 

that we may neglect L 2 as compared to D 2 , the foregoing becomes 

%m.m' .l.L 

D" 

But 2mL is the magnetic moment of NS and 2m'l is that of ns, 

hence the turning moment reduces to 

2M.M' 

L> 3 

If, in accordance with what we have assumed above, ns be very 

small in comparison to D, the field about ns is uniform, and if ns 

be deflected through an angle 8, the turning moment becomes 

2M.M' 
D * - cos5 

150. Measurement of Strength of Magnetic Field. — From 
Par. 130 we have seen that if a needle of magnetic moment M ' be 
placed in a field of strength H and be deflected through an angle 
8, the moment which tends to restore it to the meridian is 

M'.#.sin<5 



MAGNETISM. 



117 



and from the preceding paragraph we have seen that when such a 
needle, ns, and a magnet, NS, are placed in the relative positions 



'A 



V 



Fig. 75. 



n 



I 



as shown in Fig. 75, the turning moment due to the magnet is 

2M.M f 



D'< 



cos 



When equilibrium is reached these two moments are equal, 

2M.M' 



hence 
hence 



D 3 



M 
H 



cos<5 = M'.H. sind 
= -pr . tan 8 



D and 5 may be measured directly and we thus obtain a second 
expression involving M and H, which, when combined with the 
expression deduced in Par. 148, enables us to determine H. 

The needle ns being very small, a graduated circle over which 
its ends might travel could not be read with much accuracy, there- 
fore, the angle 8 is usually determined by observing the movement 
over a scale of a beam of light reflected from a tiny mirror attached 
to the needle. This method of reading the deflection of a needle 
will be more fully explained in the description of the mirror gal- 
vanometer (Par. 377). 



118 ELEMENTS OF ELECTRICITY. 



CHAPTER 15. 

THEORY OF MAGNETISM. 

151. Magnetism. — As in the case of electricity, we must at the 
outset admit that we do not know what magnetism is. It is not 
matter yet in its manifestations it must always be associated with 
matter. Gilbert called attention to the fact that with one magnet 
we could make hundreds of others and yet the strength and weight 
of the original magnet would be unaltered. We can conceive of 
no form of matter which could thus be dipped out or drawn from 
indefinitely and yet the original source of supply be undiminished. 
It is not electricity. A charged body placed in a magnetic field 
is not on account of its charge acted upon in any different way, nor 
is a magnetized body placed in an electric field attracted or re- 
pelled in any different manner on account of its magnetism. An 
electric current does however produce certain magnetic effects, 
and mechanical energy expended in moving or varying magnetic 
fields may be transmuted into electric energy. We may say then 
that with electric currents we can produce magnetism and from 
magnetism we can produce electric currents. 

Magnetic forces pass with equal ease through the hardest sub- 
stances, the thinnest gases and a vacuum. The medium concerned 
in this propagation is therefore considered to be the ether. 

152. Molecular Magnetism. — We have already seen (Par. Ill) 
that if a bar magnet be broken across, one surface of this fracture 
will be of north polarity, the other of south, and this no matter at 
what point the bar be broken nor how the line of fracture runs 
across. If these portions be again broken, the resulting fragments 
will still possess polarity and even if the final result be dust the 
ultimate particles will still be little magnets. The inevitable con- 
clusion is that the individual molecules are themselves magnets 
and that they are arranged with their like poles all pointing in one 
direction. This affords a satisfactory explanation of the fact that 
the free magnetism resides mainly at the poles, for at any inter- 
mediate cross-section the magnetism on one side of the section is 



MAGNETISM. 119 

exactly balanced and neutralized by that on the other, consequent- 
ly, the end layers are the only ones free to cause external effect. 

153. Ewing's Theory. — Two hypotheses have been advanced 
to account for the arrangement of the molecular magnets. First, 
before a steel bar is magnetized its molecules are unmagnetized 
and the act of magnetizing imparts to them their magnetism and 
arrangement. This throws but little light on the matter. Second, 
the molecules possess magnetism as an inherent property and are 
always magnetized but are indiscriminately arranged or rather 
are arranged in little groups satisfying each other's polarity and 
thus neutralizing each other's magnetic effects and producing 
little or no external magnetism. The act of magnetizing simply 
turns these molecules until their like poles point in one direction. 
The maximum effect would be produced when all of the molecules 
had been turned and the magnet is then said to be saturated. 

This theory was first advanced by Weber and later elaborated 
by Ewing, whose name it bears. The latter showed that it satis- 
factorily accounts for the known facts of magnetization, especially, 
as will be seen later (Par. 395), for the varying rate of change of 
magnetism accompanying a constant rate of change of the mag- 
netizing force. Certain corroborating phenomena are described 
in the following paragraphs. 

An explanation of magnetism based upon the electron theory 
(Par. 27) is now being elaborated but is not yet thoroughly 
developed. 

154. Magnetization is Accompanied by Molecular Movement. 

* (a) If a small glass tube be filled with steel filings and then 
subjected to magnetization, the filings will be seen to arrange 
themselves end to end and thereafter the tube will act as a magnet. 
This is thought to be analogous to what takes place among the 
molecules of a magnetic body during magnetization. If the filings 
be shaken up and disarranged the magnetism disappears. 

(b) When an iron bar is suddenly magnetized by an electric 
current a metallic clink is heard. This could be produced only 
by a vibration among the molecules of the bar. 

(c) When an iron bar is rapidly magnetized and demagnetized 
it grows hot. This heat could be produced only by internal move- 
ment among the molecules. 

(d) Magnetization is accompanied by a change in the dimen- 
sions of the magnetic substance. An iron bar strongly magnetized 



120 ELEMENTS OF ELECTRICITY. 

increases 1/720,000 of its length but if still more strongly magnet- 
ized it contracts again. A bar of cobalt at first diminishes and 
then increases. Nickel diminishes from the first. The change in 
dimensions must result from movement among the molecules. 

155. Freedom of Molecular Movement Facilitates Magneti- 
zation. — When a magnetic body is placed in a magnetic field, we 
may consider that a force is tugging at each of the little molecular 
magnets endeavoring to turn them so that their like poles will 
point in one direction. This turning is impeded by the crowding 
of the molecules or by what may be designated molecular friction. 
If this crowding or friction be relieved in any way, as by vibration, 
by heating or by liquefaction, magnetization is rendered much 
easier. 

It has long been known that hard steel is very much more 
difficult to magnetize than soft iron but that once magnetized it 
retains its magnetism much better, or, as this last is usually 
expressed, its retentivity is much greater than that of iron. We 
may consider that the molecules of the rigid steel offer more 
resistance to turning than do those of the soft iron, and on account 
of this same rigidity they remain more persistently in the position 
into which they have been turned. A piece of pure iron loses its 
magnetism as soon as the magnetizing force is discontinued. The 
iron generally used in electrical machinery is not absolutely pure 
and some traces of magnetism persist after the cessation of the 
magnetizing force. This residual magnetism plays an important 
part in certain electric machines. 

156. Magnetization Facilitated by Vibration. — Vibration, how- 
ever produced, is favorable to loosening up the molecules of a body. 
Gilbert discovered that if an iron bar held in the magnetic merid- 
ian be struck with a hammer it becomes a magnet, but no such 
effect is produced if the bar be held crosswise. 

The steel columns employed so largely in modern buildings are 
all planted in the meridian and in accordance with the principle 
stated in Par. 143 are penetrated lengthwise by the lines of force 
of the earth's field (see Fig. 76). They are subjected to continual 
vibration and therefore become in course of time highly mag- 
netized. The lower ends of all such columns in the northern 
hemisphere, being the ends from which the lines of force emerge, 
are north poles (Par. 142). This also explains the fact which 



MAGNETISM. 



121 



several centuries ago caused great wonderment, that is, that iron 
crosses on church steeples and the iron rods of weather vanes are 
often found to have acquired magnetic properties. 




Fig. 76. 

157. Loss of Magnetization Facilitated by Vibration. — Reflec- 
tion will show that the foregoing principle works both ways, that 
is, if an iron bar be placed in the meridian and jarred it acquires 
magnetism; on the other hand, if a magnet not in the meridian 
be jarred it loses its magnetism. Great care must then be observed 
in handling magnets not to jar them by striking or by dropping 
or otherwise, as under such conditions they deteriorate rapidly. 
Even if a magnet be in the meridian when jarred, it loses strength 
for the earth's field, being much weaker than the magnetic field 
originally used in making the magnet, can not hold in position all 
of the molecules when they begin to vibrate. 

158. Effect of Heat. — It is known that when a body is heated 
its molecules are put into more or less violent vibration. When a 
magnetic body is heated to a red heat the vibrations reach such a 
pitch that they are no longer controlled by magnetic force, that 
is, its molecules are dancing about so that the magnetic force can 
no longer pull them into line, therefore, at a red heat magnets lose 
their magnetism and magnetic bodies are no longer attracted and 
can no longer be magnetized. If, however, such heated bodies be 
allowed to cool in a magnetic field, the molecules as they quiet 
down take positions in accordance with the magnetic force and the 
result is that the bodies acquire magnetism. Gilbert found that 
bars of iron or steel heated to redness and allowed to cool in the 



122 ELEMENTS OF ELECTRICITY. 

meridian became magnets. If molten cast-iron be run into a 
mould and cools and solidifies in a strong magnetic field it acquires 
magnetism. 

159. Magnetization Facilitated by Solution. — When a body is 
in solution it is separated into its individual molecules and these 
have great freedom of movement. Deposition from solution 
must take place 4 molecule by molecule. Should a magnetic sub- 
stance in solution be deposited while in a magnetic field, the 
molecules should have no trouble in arranging themselves and the 
resulting body, if our hypothesis be correct, should exhibit marked 
magnetic properties. This has been confirmed experimentally by 
depositing iron electrolytically (as electroplating is done) in a 
strong field. 

We are taught by geology that beds of iron ore are accumulated 
through chemical processes by deposition from solution. Since 
this deposition takes place in the earth's magnetic field, this 
affords a reasonable explanation of the occurrence of the lode- 
stone. Gilbert, although he wrote long before the atomic theory 
had been advanced, evidently had this thought in mind and in 
Chapter II, Book III of his work gives the following significant 
experiment. "We once had chiselled and dug out of its vein a 
lodestone twenty pounds in weight, having first noted and marked 
its extremities; then after it had been taken out of the earth we 
placed it on a float in water so it could freely turn about; straight- 
way, that extremity of it which in the mine looked north turned to 
the north in water and after a while there abode." 



MAGNETISM. 123 



CHAPTER 16. 

MANUFACTURE OF MAGNETS. 

160. Most Suitable Metal for Making Magnets. — We have 
stated that soft iron is far more easily magnetized than steel but 
on the other hand its retentivity, or power of retaining imparted 
magnetism, is very slight. The best permanent magnets are made 
from glass-hard steel, that is, steel which has been heated to a 
bright red and then plunged into cold water. Certain metals 
alloyed with steel improve its magnetic properties and others 
injure or destroy them. An alloy of tungsten produces magnets 
of great retentivity, while an alloy of manganese can hardly be 
magnetized at all and has been proposed for structural work in 
electrical laboratories. 

161. Principle of Manufacture of Magnets. — We have seen 
that in theory a bar of steel becomes a magnet when its molecules 
have been turned so that their poles lie in one direction. The 
manufacture of magnets is based upon this theory, and just as we 
get the individual hairs of a piece of fur to lie in one direction by 
combing or by brushing or by blowing upon the fur, so we, in a 
sense, comb or brush or blow the molecules of the bar of which 
we wish to make a magnet. The principle of these processes is 
the same; they differ merely in details of execution. 

162. Magnetization by Single Touch. — In this method the bar 
to be magnetized is placed horizontal and preferably with its ends 



? N| is N| |s \ 

resting upon or just in front of opposite poles of two magnets as 
shown in Fig. 77. It may then be stroked from end to end with a 
magnet, using the pole of the same kind as that near which the 



124 ELEMENTS OF ELECTRICITY. 

last touched end of the bar is resting. A better way is to begin at 
the middle of the bar and stroke it, the stroking magnet following 
the path shown by the dotted line in the figure, then reverse ends 
of the stroking magnet and stroke the other half of the bar in the 
opposite direction. Finally, turn the bar over and repeat the 
strokings upon the other side. The point last touched is of 
opposite polarity to the pole with which it is stroked. 

163. Magnetization by Divided Touch. — This method is in 
principle precisely the same as the foregoing and differs only in 
that two magnets are used in the strokings. The opposite poles 
of the two magnets are placed at the center of the bar (Fig. 78) and 




are then drawn apart, the magnets following the paths shown by 
the dotted lines in the figure. After eight or ten strokes, the bar 
is turned over and the other side is stroked. Sometimes a block 
of wood is placed between the poles of the stroking magnets and 
they are held against this and slid back and forth along the bar, 
being finally removed at the center of the bar. This last is called 
the method by double touch. 

164. Magnetization by an Electric Current. — The best method 
of magnetization is by means of an electric current. An insulated 
wire is coiled around the bar to be magnetized and a current is 



Ax^> 



Fig. 79. 

sent through the wire. As result of this treatment the bar be- 
comes a magnet. A full explanation of this can not be given 
without anticipating certain principles which have not yet been 
developed and it must therefore be deferred until later, but it can 
be stated that if a current flows through the coiled wire as shown 
diagrammatically in Fig. 79 and in the direction of the small 



MAGNETISM. 125 

arrowheads, there will be produced inside of the hollow of the coil a 
magnetic field whose lines of force run as shown by the large arrow, 
that is, inside of this hollow space around which the coil is wrapped 
lines of force will run like a draught runs up a chimney and an 
iron or steel bar placed in this field will have its molecules all 
swept or "blown" into a common direction, and in the case of 
steel a great part of them retain this new position. They really 
turn in accordance with the principle given in the latter part of 
Par. 144. 

165. Consequent Poles. — If a magnet be touched at some 
point between its poles by a second magnet, the molecules around 
that point may be disarranged to the extent of producing poles 
intermediate to the original ones. Such intermediate poles are 
called consequent poles. They are usually the result of some 
accident or error in the process of magnetization. Their presence 
may be detected by exploring the field about the magnet by means 
of a small compass needle or by use of the magnetic figures. They 
may be intentionally produced by stroking the bar in a different 
manner from that prescribed or, in the electric method, by wrap- 
ping a portion of the coil in opposite direction to the rest. If, for 
example, a steel knitting needle be stroked with the north pole of 
a magnet, the strokes beginning at each end and terminating at 
the center, the needle will be found to have a north pole at each 
end and a south pole at the center. 

166. Magnetization Largely Confined to Outer Layers of 
Magnet. — The process of magnetization effects the outer layers 
of the steel bar more than it does the interior portions. This may 
be shown in several ways. If a magnet be placed in acid and its 
outer layer be dissolved off, its magnetism will be found to de- 
crease at a more rapid rate than its mass. Again, if a number of 
thin flat pieces of steel, as for example blades of table knives, be 
bound up in a bundle and magnetized, it will be found when the 
bundle is taken apart that those on the outside of the bundle are 
much more strongly magnetized than those on the interior. There 
are three reasons for this. First, when the magnetism is imparted 
by stroking, the outer layers act as a magnetic screen for the inner 
layers (Par. 143), that is, the teeth of our magnetic comb do not 
reach down into the deeper layers of molecules. Second, when the 
electric method is used, the field is stronger close to the wire than 



126 ELEMENTS OF ELECTRICITY. 

it is in the center of the coil so the outer portions of the bar become 
more highly magnetized. Third, the outer layers act by induction 
upon the inner layers and tend to produce in them an opposite 
polarity, thereby weakening them. This last may be shown as 
follows. If three similar steel bars be magnetized equally and then 
tied together and used as a magnet, when they are again taken 
apart the inner one will be found to be weaker than the outer ones. 
Since thin ribbon-like bars can be more thoroughly magnetized 
than thicker ones, the most powerful magnets are made of a 



Fig. 80. 

number of these separately magnetized and then bound together. 
Such laminated magnets are powerful but, for reasons just explained, 
their power does not increase in direct proportion to the number 
of lamina? or strips. It is found best to have the interior layers 
project, as shown in Fig. 80, slightly beyond the outer layers. 
Sometimes the ends of such magnets are inserted into soft iron 
pole pieces. 

167. Aging of Magnets. — Even if they are handled carefully 
and not jarred, magnets grow weaker with time, most probably on 
account of the inductive effect mentioned in the preceding para- 
graph, and may take several years to attain a constant state. In 
certain electrical measuring instruments in which magnets are 
used, it is of the utmost importance that these retain a constant 
strength. Such magnets can be put through an artificial process 
of aging by which the constant state can be reached quickly. This 
treatment consists in exposing the newly made magnet to a current 
of steam for some 20 hours, then remagnetizing it and exposing it 
again to steam for ten hours. 



MAGNETISM. 127 



CHAPTER 17. 
TERRESTRIAL MAGNETISM. 

168. Location of Earth's Magnetic Poles. — We have seen that 
Gilbert made the discovery that the earth itself is a magnet. 
Starting from this point we are naturally led to enquire where are 
its poles, what is the direction and intensity of its field at different 
localities and, finally, why is it a magnet. 

In experimenting with his spherical lodestones or terrellas Gil- 
bert located their poles as follows. He laid a short piece of iron 
wire upon the surface of the terrella near its equatorial region. 
The wire became a magnet by induction and turning on the 
polished surface of the sphere, as if on a pivot, pointed toward the 
pole. The direction in which the wire pointed was marked with 
chalk and the wire was then shifted to some other position and its 
direction again marked. These chalk lines prolonged intersected 
at the poles. Were the earth a homogeneous sphere its magnetic 
poles could probably be located similarly, that is, the direction in 
which a magnetic needle pointed at various localities could be 
determined and these direction lines prolonged would intersect 
at the poles, but the earth is far from being such a sphere and a 
series of needles distributed around a parallel of latitude would 
indicate directions not even approximately converging. 

If we should start at any point with a magnetic needle and 
move it continually in the direction of its length, just as is done 
in the method described in Par. 141, we would not trace the arc of 
a great circle but a curved line which if prolonged in both direc- 
tions would eventually pass through the magnetic poles. Two 
such lines would by their intersections locate the poles. 

Figure 81 represents a portion of the northern hemisphere with 
a series of such curves which begin at points along the equator 
ten degrees apart. It will be noted that the north magnetic pole 
does not coincide with the geographical pole and is in fact nearly 
twenty degrees, or some twelve hundred miles, south of the latter. 
It was discovered by Sir J. C. Ross during the arctic expedition 
of 1829-33 and is located on the Island of Boothia Felix, north of 



128 



ELEMENTS OF ELECTRICITY. 



Hudson Bay, in latitude 70° 5' north and longitude 96° 43' west. 
The south magnetic pole has not been reached. It is located in the 
antarctic regions in approximately latitude 73° 30' south and 
longitude 147° 30' east, whence it is seen that the two magnetic 
poles are not at the extremities of a diameter of the earth. 

It follows from the foregoing that what we have designated in 
the preceding pages as the magnetic meridian, or the vertical plane 
through the axis of the poised needle, does not in general pass 
through the magnetic poles and furthermore changes its direction 
from point to point. 




169. Magnetic Declination. — A study of Fig. 81 will show that 
within its limits there are three and only three regions in which 
the needle points to the geographic north pole. These regions, 
marked A, B and C on the map, are the western side of Hudson 
Bay, the vicinity of St. Petersburg in Russia and the eastern 
portion of Siberia. At other points the needle points either to the 
east or to the west of the true meridian. Thus, along a parallel 
from St. Petersburg to Hudson Bay the needle points to the west 
of the meridian, while continuing from Hudson Bay to Siberia it 



MAGNETISM. 129 

points to the east. This deviation of the needle from the true 
meridian is called the magnetic declination. We shall see later that 
the declination at any locality is slowly changing. In 1905 along 
a line through Charleston, S. C, Cincinnati, Ohio, Lansing, 
Michigan, and thence across Lake Superior the needle pointed 
true north, while in the northeast corner of Maine the declina- 
tion was 21° west and in the extreme northwest of the State of 
Washington it was 24° east. The magnetic declination is some- 
times called the magnetic variation, but there are several kinds of 
magnetic variation and the term declination is to be preferred. 

170. Isogonic Chart. — It is of the utmost importance that 
navigators should know the magnetic declination at whatever 
point their vessel may be. For example, if a vessel be off the mouth 
of the Columbia River and its captain wishes to sail due north, 
he must steer by compass 22° to the west of north. A knowledge 
of the declination is also required by surveyors. Information of 
this kind is often given graphically in so-called magnetic maps. 
One of these, for the year 1905, is shown in Fig. 82 and is prepared 
by joining by a continuous line all those points at which in that 
year the declination was the same. The resulting curves are 
called isogonic lines (lines of equal declination) and the map is 
called an isogonic chart. The heavy lines are the agonic lines, or 
lines of no declination; the lighter lines are those of westerly 
declination; the dotted lines are those of easterly declination. It 
will be noted that there is one agonic line completely encircling 
the earth (shown as two in the Mercator's projection used in the 
chart) and a second one embracing an elliptical area in eastern 
Asia. This last is called the Siberian oval. 

Figure 83 is the isogonic chart for the United States for the year 
1905 taken from the report of the Superintendent of the Coast 
Survey for 1906. 

171. Magnetic Dip. — In manufacturing needles for compasses 
and surveying instruments, they are shaped and finished off while 
the metal is soft, after which they are tempered glass hard and 
then magnetized. They are carefully balanced before being- 
tempered for afterwards they are too hard to file and grinding 
would injure their magnetization. Robert Norman, an instrument 
maker of London, noticed in 1576 that no matter how carefully 
he balanced his needles they were thrown out of balance after 



130 



ELEMENTS OF ELECTRICITY. 




MAGNETISM. 



131 



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132 ELEMENTS OF ELECTRICITY. 

being magnetized and invariably the north end appeared to be 
the heavier so that he was compelled to restore the balance by 
sticking a small piece of wax under the south end. Being angered 
one day, or as he expressed it "being stroken into some choler," 
by ruining a needle upon which he had expended a good deal of 
labor and whose balance he endeavored to restore by cutting off 
a small piece from the north end, he began to reflect upon the 
matter and finally made a needle which, before being magnetized, 
balanced on horizontal trunnions. After magnetization, the 
north end dipped down until the needle stood at an angle of 72° 
with the horizontal plane. The angle which the axis of such a 
needle makes with the horizontal plane is called the magnetic dip 
or magnetic inclination. The explanation of the magnetic dip is 
as follows: The lines of force of the earth's magnetic field not 
being circles and its poles being at some unknown depth, these 
lines of force are not parallel to the surface but penetrate it, in 
other words, they are inclined to the plane of the horizon. A 
magnetic needle free to move in a vertical as well as in a horizontal 
plane will place itself tangent to the lines of force and the angle 
which these lines make with the horizontal plane is the magnetic 
dip. As in the case of the declination, the dip is slowly changing. 

The lack of balance in the needles of engineering instruments 
is frequently corrected by wrapping a fine silver wire about the 
south end of the needle. 

172. Dipping Needle. — A needle arranged to measure the angle 
of dip is called a dipping needle. One of these is shown in Fig. 84. 
The needle is ten or twelve inches long and is mounted upon a 
steel knife-blade axis resting upon polished agate bearings. For 
still more delicate observations an instrument is used in which the 
needle is suspended at the center of a complete graduated circle 
which may be rotated about a vertical axis and which, like a 
surveyor's transit, is furnished with a slow motion screw by 
which it may be accurately placed in the meridian. The angles 
are read by verniers and microscopes and observations are mul- 
tiplied so as to eliminate instrumental errors. For example, to 
correct for the error due to the line joining the 90° marks at the 
top and bottom of the graduated circle not being vertical, the 
angle marked by the needle is read, the circle is then rotated 180° 
around its vertical axis, the angle is again read and the mean of 
these observations is taken. To correct for the error due to the 



MAGNETISM. 



133 



axis of suspension of the needle not corresponding with the center 
of the circle, both ends of the needle are read and the mean of these 
readings is taken. To correct for 
error due to the magnetic axis of 
the needle not corresponding with 
its geometric axis, the above ob- 
servations are repeated with the 
needle reversed from back to front 
and these readings are combined 
with the former ones. To correct 
for error due to lack of mechanical 
balance in the needle, observations 
are made, the needle is then de- 
magnetized and remagnetized in 
the opposite direction, placed in 
position, a second set of observa- 
tions taken and the means of the 
two sets combined. There are 
observed other refinements not 
necessary to mention here. 




173. Isoclinic Chart. — Figure 85 
represents a section of the earth 
by a plane passing through its axis 
and the north magnetic pole. The 
arrows represent the position of the dipping needle at the corre- 
sponding points. At the magnetic poles the dip is 90° or the 



Fig. 84. 




Fig. 85. 



needle stands vertical and this was one of the observations by 
means of which the north magnetic pole was located. Along 



134 



ELEMENTS OF ELECTRICITY. 




MAGNETISM. 135 

the magnetic equator, which in the western hemisphere lies south 
of the geographical equator, the dip is zero or the needle lies 
horizontal. Lines connecting those points on the earth's surface 
where the dip is the same are called isoclinic lines. An examina- 
tion of the isoclinic chart, Fig. 86, will show that these lines 
run generally east and west but curve irregularly and are not 
parallel. 

174. Magnetic Intensity. — The strength of the earth's field, 
or the magnetic intensity, can not easily be measured directly but 
by the method outlined in Pars. 148, 149 and 150 we may deter- 
mine its horizontal component, whence, since the total intensity 
is equal to this horizontal component divided by the cosine of the 
angle of dip, the total intensity is readily calculated. 

Having determined the horizontal component at one point, it 
may easily be determined at any other by applying the method 
by oscillations as described in Par. 129. The same magnetic needle 
is oscillated for the same period of time at the two places and the 
number of oscillations counted; the horizontal components at the 
two places are to each other as the square of the number of oscil- 
lations executed in equal intervals of time. 

The horizontal component is greatest along the magnetic equa- 
tor but varies at different points along this line. It is a maximum 
over a region embracing a part of India, the Malay Peninsula 
and the Islands of Borneo and New Guinea, its strength being 
.38, that is, a unit pole placed in the earth's field in this region 
would be urged in a horizontal direction with a force of .38 dynes. 
At the magnetic poles the horizontal component is zero and near 
these points the total intensity is determined from the vertical 
component instead of from the horizontal. The total intensity 
increases from the equator towards the magnetic poles. It is 
however not a maximum at these poles but in each hemisphere at 
two points or magnetic foci. In the northern hemisphere one of 
these points is just south of Hudson Bay, the other is in north 
central Siberia. In the southern hemisphere both points are to 
the south of Australia. The maximum value in the northern 
hemisphere is about .65 and in the southern about .70. Just as 
with the declination and the dip, the total intensity is found to be 
slowly changing. 

Lines connecting points of equal horizontal intensity or of equal 
total intensity are called isodynamic lines, and isodynamic charts 



136 



ELEMENTS OF ELECTRICITY. 



are prepared in a similar manner to the isogonic and isoclinic 
charts. 

175. Magnetic Elements. — The declination, the dip and the 

magnetic intensity at any given point are termed the magnetic 
elements of that point. As observations are multiplied, our knowl- 
edge of these elements and of the laws of their variation corre- 
spondingly increases. In the report of the Superintendent of the 
Coast and Geodetic Survey for 1906, data is presented from ac- 
curate observations at 3500 stations, or from every 30 miles 
square of the U. S. territory. The following table, extracted from 
this report, gives the declination, dip and horizontal intensity at 
various localities as determined by observations made in the year 
ending June 30, 1906. 



TABLE OF MAGNETIC ELEMENTS. 

1905-1906. 

Locality Declination Dip Hor. Intensity 

Albany, N. Y 11° 08' W 73° 50' . 16939 

Ann Arbor, Mich 2° 01' W 72° 51' . 18248 

Baltimore, Md 5° 55' W 70° 42' . 19560 

Bangor, Me 17° 28' W 74° 50' . 15715 

Columbia, S. C 0° 0' 65° 35' .23791 

Fargo, N. D 11° 30' E 75° 35' .15731 

Galveston, Tex 7° 28' E 58° 37' .28404 

Green River, Utah 15° 40' E 66° 08' .23476 

Helena, Mont 19° 49' E 72° 08' . 18548 

Honolulu 10°35'E 39° 20' .29566 

Joliet, 111 2° 52' E 72° 13' . 18857 

Key West, Fla 2° 31' E 55° 03' . 29404 

Los Angeles, Cal 15° 14' E 59° 31' .26902 

Memphis, Tenn 5° 30' E 65° 47' .24080 

Montreal, Can 14° 40' W 75° 38' . 15122 

New York, N. Y 9° 08' W 72° 02' . 18690 

Philadelphia, Pa 7° 45' W 71° 04' . 19361 

Portland, Ore 22° 44' E 68° 39' .21754 

San Francisco, Cal 17° 00' E 62° 43' .24898 

Silver City, N. M 12° 46' E 59° 51' .27301 

Sitka, Alaska 30° 01' E 74° 42' . 15494 

Washington, D. C 4° 34' W 70° 28' . 20022 



MAGNETISM. 



137 



176. Variation of the Magnetic Elements. — The magnetic 
elements at any locality are far from being constant. They pass 
through cycles of variation with periods of years, through others 
with the seasons, still others in each twenty-four hours and finally 
others at irregular intervals. These variations may therefore be 
classed as periodic and irregular, the first class embracing the 
secular, the annual and the diurnal variations. Although all of 
the elements vary, it is only to the variation in declination, and 
furthermore only to the secular variation of this element, that 
any practical importance attaches. 

177. Secular Change in Declination and Dip. — For over 300 
years it has been noted that the declination and dip were slowly 
changing. In 1580 at London the declination was 11° 17' east and 
was decreasing so that in 1657 the needle pointed true north. The 



1500 



1600 



1700 



1800 



1900 



2000 



variation 
20° 



west 
10° 



0° 



variation east 
10° 20° 



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Fig. 87. 



movement continued in the same direction until in 1816 a maxi- 
mum westerly declination of 24° 30' was reached and retrogression 
began. In 1900 the declination was 16° 16' west. This movement 
is shown graphically by the curve in Fig. 87. In about the year 
1976, or some 320 years since the needle last pointed true north, it 
should again point north, but since the curve shows that the 



138 ELEMENTS OF ELECTRICITY. 

westerly variation is greater than the easterly, the period of a 
complete cycle will not be known until the needle moving westward 
again points to 11° 17' as in 1580. 

The change in declination is accompanied by a change in dip, 
although the angular range of the dip is much less than that of the 
declination. At London the total variation in dip has been 7° 33' 
while that in declination has been 35° 47'; however, the range in 
dip is still increasing which is not true of the range in declination. 
To the eye of the observer placed at the pivot of the needle in 
London, the north pole of the needle would appear to have traced 
in a clockwise direction since 1580 about two-thirds of a more or 
less irregular and flattened oval. This fact, taken alone, would 
seem to indicate that the north magnetic pole viewed from some 
point outside of the earth is slowly rotating in a counter-clockwise 
direction around some undetermined point in the northern regions. 

As we travel around a parallel of latitude we find, as has already 
been shown, that the declination differs at different points and is 
changing. We also find that both the direction of change and the 
rats of change vary from place to place. Thus (Fig. 83) across 
the northeast of Maine in 1905 the declination was 20° west and 
was increasing 4' per year; along the agonic line through South 
Carolina the declination was varying westerly 2' per year; along 
a line through Alabama, Illinois and Wisconsin the declination 
was stationary; along the Mississippi Valley it was increasing 
easterly V per year; along the crest of the Rocky Mountains it 
was increasing easterly 3' per year and on the coast of Oregon, 
where the declination was 20° east, it was increasing easterly 4' 
per year. These changes indicated that the isogonic lines were 
slowly crowding in upon the agonic line and that the north mag- 
netic pole was moving southward. As observations increase we 
may be able in time to speak with more certainty of these move- 
ments. 

178. Diurnal Change in Declination. — The magnetic elements 
are subject to slight daily changes and these changes are more 
satisfactorily studied by means of self recording instruments. 
For instance, a needle suspended by a delicate silk fibre carries a 
small concave mirror upon which falls a beam of light from an 
electric bulb. This mirror reflects a brilliant spot upon a roll of 
photographic paper which is unwound at a known rate by clock- 
work. As long as the needle is motionless, the trace of the spot 



MAGNETISM. 



139 



upon the sensitized paper is a straight line but any movement of 
the needle produces a curve. Fig. 88 represents such a record 
made near London in 1900. At 8 A. M. the declination was least 
but increased steadily until about 2 P. M. when it reached a 
maximum. It then decreased until 8 P. M. when it was nearly 
stationary for about an hour and then began to decrease again 
and continued until 8 A. M. A similar record would be made at 
all points, no matter whether the local declination be east or west, 
but the direction of movement in the southern hemisphere is the 
reverse of that in the northern. Along the equator the daily 



\z 



J2 



JZ 



I 



P.M. 



PH. 



P.M. 



Fig. 88. 



range of the needle does not exceed 4' while in northern Europe 
it reaches 15'. 

The dip, registered in a similar manner, is found to be about 5' 
greater in the morning than in the afternoon. 

179. Annual Change in Declination. — If the average declination 
for each month be obtained from the self -registering instruments 
and these monthly averages be compared among themselves, it 
will be seen that in the northern hemisphere the needle moves to 
the west from May to September and to the east from September 
to May. In the southern hemisphere these movements are re- 
versed and in either case they are but slight. 

180. Magnetic Storms. — It has long been known that in addi- 
tion to the periodic variations described in the preceding para- 



140 



ELEMENTS OF ELECTRICITY. 



graphs, magnetic needles are not infrequently subject to other 
variations occurring at irregular intervals. If a needle be observed 
at such a time it will be seen to waver or tremble and to fluctuate 
through an angle varying from a few minutes to one degree and in 
extreme cases even to two to three degrees. The variation is only 
momentary but may be often repeated. Such disturbances are 
called magnetic storms. They occur simultaneously at the most 
distant points and involve all the magnetic elements. Their 
effects are best studied by means of the curves traced as described 
in Par. 178. The record instead of being the sinuous curve as in 
Fig. 88 is jagged and irregular. These storms occur more fre- 
quently at night than during the day and are also more frequent 
in summer than in winter. They are especially marked during 
auroral displays and it was for a time thought that the two phe- 
nomena were related as effect and cause, but it is now held that 
they have a common cause. 




1810 



1830 1840 1850 
Fig. 89. 



18.60 1870 



In 1852 it was observed that the periods of maximum frequency 
of magnetic storms coincides with the maximum occurrence of 
sun spots, both taking place every eleventh year. This coin- 
cidence is shown graphically in Fig. 89 in which the full line shows 
the relative number of sun spots for each year and the broken line 
the number of magnetic storms. The agreement is too close to be 
accidental. 

181. Theories of the Earth's Magnetism. — There is no accepted 
theory of the earth's magnetism but since, as we have seen above, 
its manifestations are periodic in character, these periods corre- 
sponding to the diurnal and annual time periods of the earth and 



MAGNETISM. 141 

to the eleven year period of the sun spots, the indications are that 
its source is the sun. The significance of the declination period 
has not yet been grasped, in fact, as was pointed out (Par. 177), 
we can not be sure for a number of years to come what is the 
exact length of this period. Could it be shown that electric cur- 
rents flowed around the globe from east to west, this, as will be 
seen in electro-magnetics, would account for the magnetic phe- 
nomena and this explanation was advanced and elaborated by 
Ampere. So-called earth currents are known to exist but their 
direction is along the meridian instead of across it. It is known 
that electricity is produced both by heat and by evaporation, also 
that the magnetic properties of bodies are effected by heat, and it 
is conceivable that the sun as in its apparent motion it sweeps 
along overhead at the equator at the rate of 1000 miles per hour 
may produce successive masses of charged vapor which might 
have an effect similar to a current, and also that the warming of 
successive portions of the earth's crust may alter its magnetic 
properties sufficiently to account for the diurnal and seasonal 
variations. An additional fact which points to this hypothesis is 
that the isothermal lines, or lines of equal average temperature of 
the earth's surface, correspond closely in direction with the 
isoclinal lines. 

Faraday, in investigating paramagnetic and diamagnetic bodies, 
discovered that oxygen is magnetic and that its magnetism in- 
creases as it grows colder. He therefore suggested that the oxygen 
of the atmosphere is naturally magnetic and that the variations 
produced in its magnetism by the daily and seasonal variations 
in temperature would afford a satisfactory explanation of the 
periodic variations of the needle. 

Other theories have been advanced but they can not be regarded 
as much more than speculations. 

182. The Mariner's Compass. — In the surveyor's compass, a 
long, slender needle is pivoted free to rotate within a horizontal 
circle which is so graduated that the north end of the needle points 
to the angle which the line of sight of the telescope makes with the 
magnetic meridian. Since the graduated circle and the telescope 
rotate together about the vertical axis of the instrument, the 
needle remaining motionless, the west half of the circle must be 
marked east and the east half must be marked west. 



142 



ELEMENTS OF ELECTRICITY. 



The mariner's compass (Fig. 90) is differently arranged, the 
graduated scale being fastened to the needle and rotating with it 
and hence the interchange of east and west not being necessary. 
The pointer which indicates the direction in which the vessel is 




Fig. 90. 

sailing is a vertical mark on the inside of the box in which the 
compass turns. In the compass perfected by Lord Kelvin there 
turns upon an iridium needle point a central jewelled cup to which 
is attached by tightly drawn silk threads a thin aluminum ring, 
six or eight inches in diameter, the whole resembling a wheel of 
which the cup is the hub and the threads the spokes. Upon the 
rim is fastened the paper scale divided into the customary 32 
"points of the compass/' and also with an outer graduation in 
degrees. The needle proper consists of eight separate needles, 
slender bars about three inches long, arranged like the rungs of a 
ladder and fastened to the under side of the silk spokes, being 
symmetrically placed with respect to the jewelled cup. The com- 
pass is contained in a glass-covered, cylindrical copper box, 
weighted at the bottom and supported on gimbals. To the box 
itself there are attached two trunnions which rest upon a copper 
ring concentric with the box. This ring in turn carries two trun- 
nions which are in the same horizontal plane as the first pair and 
at right angles to them, and these in their turn rest upon a second 
and outer concentric ring. By this arrangement the compass is 
kept horizontal no matter how much the ship may roll. In order 
to slow down the oscillations of the needle, the box is often filled 
with some thick non-freezing liquid, such as glycerine, and by 
making a portion of the rim of the compass card hollow, the liquid 



MAGNETISM. 143 

will buoy up the card and relieve the pivot of a portion of the 
weight upon it. 

The compass and its box are placed upon a pedestal, called the 
binnacle, which carries the necessary lamps for reading the com- 
pass at night and also supports the magnets and masses of soft 
iron used in making correction for local disturbances of the needle. 

183. Adjustment of Mariner's Compass. — In the construction 
of vessels the use of iron and steel has largely displaced wood. 
During the building of a vessel it rests for a relatively long period 
of time at a constant angle with the earth's field and the continual 
hammering and vibration to which it is subjected converts it as a 
whole into a magnet. In addition to this, such vertical columns of 
steel as the cut water and the stern post become, as explained in 
Par. 156, magnets whose south poles, for vessels in the northern 
hemisphere, are at the upper ends and therefore about on a level 
with the deck upon which the compass stands. When such a 
vessel is launched the magnetism of the hull may entirely vitiate 
the indications of the compass. However, it has been found that 
by means of permanent magnets and of masses of iron, properly 
placed, compensation may be made for these disturbing influences. 
For example, reflection will show that a magnetic cut water and 
stern post produce no variation in the compass when the vessel 
is sailing in the magnetic meridian, either north or south, but if it 
be sailing in any other direction in the semicircles to the east or 
west, the compass will be affected. Since the error produced is in 
one semicircle always to the east and in the other always to the 
west, the disturbance is called the semicircular variation. It may 
be corrected by a vertical rod of iron or a sphere of soft iron placed 
on the opposite side of the binnacle from the vertical magnetic 
body whose influence is the stronger. Similarly, the magnetism 
of the hull may be divided into two components, one lengthwise of 
the ship, the other crosswise, and these can be separately counter- 
balanced by compensating magnets placed usually in the pedestal 
of the binnacle. In making these adjustments, the newly launched 
vessel is anchored in some known position with reference to the 
magnetic meridian and the needle is brought to its correct reading. 
The vessel is then swung through an angle of 90° and adjustments 
again made, and so on around the circle, the process being called 
swinging ship. Magnetic masses in the cargo may cause disturb- 
ances of the needle and the magnetism of the hull grows less with 



144 ELEMENTS OF ELECTRICITY . 

age and varies with the latitude, the vertical component becoming 
entirely reversed when the magnetic equator is crossed, therefore 
the navigator checks the indications of his needle by frequent 
astronomical observations and makes the necessary adjustments 
when the error becomes excessive. 

184. Magnetism to be Reverted to Later. — The subject of 
magnetism is usually treated more extensively than in the pre- 
ceding chapters. Thus, a theory of magnetic potential may be 
developed similarly to that of electric potential. It is thought, 
however, that enough of the principles have been given to enable 
the student to follow without difficulty the explanations in the 
following sections. Moreover, in view of the fact that electro- 
magnets, or magnets produced temporarily by means of the 
electric current, are for most purposes far more suitable and more 
largely used than permanent magnets, and that the phenomena 
and properties of the magnetic circuit are most markedly exhibited 
and can be most clearly explained by reference to these electro- 
magnets, it is logical that we should first take up the subject of 
electric currents. Further consideration of magnetism is there- 
fore postponed for the present. (See Chapters 31 and 32.) 



VOLTAIC ELECTRICITY. 145 



PART III. 
VOLTAIC ELECTRICITY. 



CHAPTER 18. 

DISCOVERIES OF GALVANI AND VOLTA. 

185. Galvani' s Discovery. — The discovery of current electricity, 
or rather of methods of producing it by chemical means, is as- 
cribed to two Italians, Galvani and Volta, the former Professor of 
Anatomy at Bologna, the latter Professor of Natural Philosophy 
at Pavia. 

Tradition has it that about 1786 the wife of Galvani being indis- 
posed, her physician prescribed for her a broth of frogs' legs. 
Some had been procured and skinned preparatory to cooking and 
lay upon a table near an electrical machine. Galvani's assistant 
happening to draw a spark from the machine, Madame Galvani 
noticed that at the same instant the severed legs twitched convul- 
sively and that this was repeated with every spark. She called the 
attention of her husband to this phenomenon which he imme- 
diately proceeded to investigate. We now know that these twitch-- 
ings were produced by the escape of the charge induced in the 
legs, which charge was released whenever the machine sparked, 
but Galvani, who was an anatomist and not an electrician, thought 
that he was on the verge of discovering the vital principle and 
continued his researches with this idea in mind. Having one day 
prepared several pairs of legs for experiment and wishing to place 
them to one side until they were needed, he hooked a copper wire 
through the remnant of the back bone and hung the legs to the 
iron railing of the balcony in front of his window. A light wind 
was blowing and to his astonishment he saw that whenever the 
dangling legs came in contact with the railing they were thrown 
into convulsive movement. Further experiment showed him that 
in order to produce these movements it was necessary to have two 



146 



ELEMENTS OF ELECTRICITY. 



dissimilar metals in contact and that the greatest effect was pro- 
duced when the free end of one touched a nerve at the same time 
that the free end of the other touched a muscle. He attributed 
these effects to a so-called "animal electricity" whose seat lay at 
the junction of the nerve and muscle, where, by some unknown 
vital principle, the nerve became charged positively and the 
muscle negatively, and, like the Leyden jar, were discharged when 
connected by the metals. He did not explain why two metals 
were required. 

186. Volta's Investigations. — Volta was not long in hearing of 
these experiments and, favored by his greater familiarity with 
what was then known of electricity, pursued a line of investigation 
which soon satisfied him that the true seat of development of the 
electricity was not at the junction of the muscle and the nerve 
but at the point of contact of the two metals. He found that if 
two dissimilar metals are brought together, one becomes positively 
charged, the other negatively, that is, they become of different 
potentials. This electrification by contact may be shown as fol- 
lows. In Fig. 91, A is a light flat needle suspended symmetrically 
above the gap between the semicircular plates of zinc and copper 
and free to turn about the vertical axis X. If a positive charge be 
given to A and if then the copper and zinc plates be brought into 
contact at B, either by touching them together directly or by 




Fig. 91. 



laying a piece of wire across the gap, the needle will swing away 
from the zinc and place itself above the copper, thus apparently 
showing the zinc to be positively charged or at a higher potential 
than the copper. Had the needle been charged negatively, it 
would have swung away from the copper and placed itself above 
the zinc. 



VOLTAIC ELECTRICITY. 147 

187. Volta's Contact Series. — Further investigation by Volta 
showed that for a given pair of metals at a constant temperature, 
this contact difference of potential is constant and is independent 
of the size of the pieces, of the amount of surface in contact and 
of the length of time that they remain in contact. For different 
pairs of metals, however, it varies with the particular ones used, 
and he was able to draw up a list of these, similar to the list of 
substances given in Par. 23, so arranged that any one becomes 
positively electrified when touched to those below it in the series 
but negatively electrified when touched to those above it. Volta's 
list comprised seven of the commoner metals. Such a list now 
would be headed by the alkaline metals, unknown in Volta's 
time, and would be ended by the non-metal carbon. His observa- 
tions were merely qualitative but subsequent observers have 
accurately measured these differences of potential. In the follow- 
ing list the numbers between the names indicate the difference in 
potential in volts set up between the corresponding pairs of metals 
when placed in contact: 

Zinc 

.210 volt 
Lead 

.069 volt 
Tin 

.313 volt 
Iron 

.146 volt 
Copper 

.238 volt 
Platinum 

.113 volt 
Carbon 

The difference of potential between any two metals in the series 
is the sum of the intervening numbers. Thus, with a zinc and 
copper pair, the difference would be .738 volts and between zinc 
and carbon it is 1.089 volts. 

Regarding as negative the difference of potential between any 
pair taken in reverse order from that given in the above list, it 
follows that the difference in potential between the first and last 
metals of any number in series depends only upon these two and 



148 ELEMENTS OF ELECTRICITY. 

is independent of the intervening metals or of the order in which 
they are arranged. Also, no matter how the intervening metals 
may be arranged, there is no difference of potential between the 
ends of a series beginning and ending with the same metal. 

The foregoing list might be extended to include other substances 
than the metals. For example (and this fact is extremely impor- 
tant), a difference of potential is produced between a metal and a 
liquid when brought into contact and if the liquid attacks the 
metal chemically, an electro-motive force will act from the metal 
towards the liquid. Finally, a difference of potential is produced 
when two liquids come into contact and even between solutions 
of the same substance when these solutions are of different degrees 
of concentration. 

188. Volta's Contact Theory. — While there is no uncertainty as 
to the facts as set forth above, there has been much controversy 
as to the interpretation to be put upon them. According to Volta, 
when two dissimilar metals are brought together, the surface of 
contact becomes a seat of electro-motive force which drives posi- 
tive electricity in one direction from the junction and negative 
electricity in the opposite, and this separation continues until the 
force of attraction between the dissimilar charges balances the 



- COPPER 



IMC + 



B 



Fig. 92. 

force which drives them apart. Thus in the compound bar of 
copper and zinc, Fig. 92, the zinc end becomes positively charged, 
the copper end negatively, or, the zinc end is at a higher potential 
than the copper. 

In general, when bodies at different potentials are connected by 
a conductor, there is a flow of electricity from the one of higher 
potential to the one of lower, and, unless constantly re-established, 
the difference of potential disappears. It would therefore seem 
that in this case if B be connected to A by a wire, a flow of elec- 
tricity would take place from B to A, but it can be shown that 
where the difference of potential is produced by contact as above 
and the metals are at the same temperature, it is not possible to 
get such a flow. If, for example, the connecting wire be of copper or 



VOLTAIC ELECTRICITY. 149 

of zinc, the effect is the same as if the bar in Fig. 92 had been bent 
around into a circle until the ends A and B touched, and when 
these ends touch, a contact electro-motive force is set up equal 
but opposite to the one already existing and hence just counter- 
balancing it. If the wire be of some third metal, it follows from 
Par. 187 that to whichever end of the bar it be connected, the 
electrical effect is to convert the bar into a compound one con- 
sisting of the metal of the remaining end and of that of the wire, 
and, as shown above, no current would be produced upon com- 
pleting the circuit. 

Independent theoretical considerations lead to the same con- 
clusion, for if a current flowed through the wire joining B and A 
in Fig. 92, by suitable arrangements, as we shall see later, this 
current could be made to do mechanical, chemical or thermal 
work and it is not possible that the mere touching of two metals 
should be a source of such energy. 

In conclusion we may say that even considering the method 
described in Par. 186, no convincing experimental proof of Volta's 
theory has yet been devised. 

189. Later Theory. — Examination of the series as given in Par. 
187 reveals the fact that the metals as therein arranged are in 
very nearly the order of their chemical affinity for oxygen as 
determined by thejieat produced by the combination of equiv- 
alent weights of these metals with that element. The difference 
of potential between pairs of metals therefore measures the 
difference of their affinities for oxygen, and its development may 
be explained as follows. Consider a piece of zinc in air. Under 
the influence of atmospheric moisture (Par. 281), this zinc is 
slowly tarnished or oxidized. The surrounding oxygen molecules, 
in order to combine with the zinc, dissociate into part molecules 
or ions (Par. 220) and those ions with a surplus of electrons, and 
hence negatively charged (Par. 27), combine with the metal, 
leaving in the adjacent air positively charged molecules. On 
the other hand, the zinc ions which combine with the oxygen 
have a deficit of electrons, or are positively charged, and the zinc 
remaining is therefore negatively charged. The zinc oxide 
produced is neutral. The result is, therefore, that the zinc 
becomes negatively charged and is surrounded by a layer of 
positively-charged oxygen atoms. A piece of copper would 
behave similarly but having a less affinity for oxygen it would 



150 ELEMENTS OF ELECTRICITY. 

acquire a smaller negative charge and the oxygen about it would 
be less highly charged positively. This state of affairs is repre- 
sented graphically in Fig. 93. No indication of these charges 
could be detected by an electrometer, for the charges upon the 
pieces of metal and in the surrounding air being equal and opposite 
produce no external effect. If, however, the two metals be touched 
together, they, being conductors, come at once to a common 
potential, but the air being a non-conductor, that about the zinc 



©©©© 




© © © 




Z ZINC ~ 


$ • 


- COPPER - 


© 


©©©© 


Fig. 93. 


© © © 





is left at a higher potential than that about the copper. We there- 
fore have good reason to believe that the difference of potential 
between pairs of metals as measured by electrometers is really the 
difference of potential between the layers of air surrounding the 
metals and not that between the metals themselves. This view 
is corroborated by the observed changes in the difference of poten- 
tial when pairs of metals are surrounded by other gases than air 

190. The Voltaic Pile. — By means of his condensing electro- 
scope Volta demonstrated, as he thought, the difference of poten- 
tial produced at the ends of a zinc-copper bar but was unable to 
detect any current in the wires by which he joined the ends of the 
bar. In Par. 188 above, it has been shown that there is no such 
current, but Volta, thinking that there was one but so feeble as to 
elude his instruments, sought some way of multiplying its effect 
and endeavored to combine the supposed currents from a number 
of zinc-copper pairs. He began by arranging in a pile a series of 
discs, alternately copper and zinc, but at once encountered a diffi- 
culty. According to his theory, from the junction of the bottom 
copper disc with the zinc disc above it a positive current ascended, 
a negative current descended, but when the second copper disc 
was reached this was reversed, a positive current descended and a 
negative current ascended, and so on. In other words, the upward 
currents were alternately positive and negative and alternated in 
this respect with the downward currents. With an even number 
of discs the net result was no greater than with two; with an odd 
number the net result was zero. Since these currents were sup= 



VOLTAIC ELECTRICITY. 151 

posed to originate at the surface of contact of the two metals, if 
the copper plates were separated from the zinc plate immediately 
below them, the contrary currents would be eliminated. He there- 
fore inserted between these plates a disc of cloth, 
Fig. 94, but since cloth is a non-conductor he 
moistened it with water. Water is a poor con- W///Mtiffih cloth 
ductor (Par. 276) but its ability to conduct is 
greatly improved by dissolving in it a small 




amount of salt or of acid. His invention therefore 

took the final form, as shown in Fig. 94, of a 

pile of pairs of zinc and copper discs separated HHi^illK 1 - ™ 

by layers of cloth or of blotting paper which had 

been soaked in brine or in dilute acid. The results 

far exceeded his expectations. The difference of lg ' 

potential between the top and bottom of the pile varied directly 

with the number of pairs of discs used. If the top and bottom 

discs were touched simultaneously, there was experienced a shock, 

milder than that of the Leyden jar but continuous. By means of 

wires attached to the extremities of the pile, electrical apparatus 

could be charged. If these wires were touched together and then 

separated, a spark was produced, etc. 

The voltaic pile was made known to the scientific world in March 
of 1800 and has long since been relegated to the museum shelf, but 
its invention, nevertheless, marks an epoch in the history of elec- 
tricity. It gave a fresh impetus to the science, which in the next 
few years advanced by bounds, and it put into the hands of the 
chemist a new agent which for the first time enabled him to decom- 
pose water into its constituent elements and made known to him 
the metals of the potassium and calcium groups. 

191. Volta's Circlet of Cups. — Volta soon noticed that the power 
of his pile fell off after a short use and he attributed this to the loss 
of the conducting liquid in the layers of cloth, partly by being 
squeezed out by the weight of the metal discs and partly by evapo- 
ration. To remedy this he devised a plan which will be under- 
stood from the following explanation. Let us suppose the pile to 
be laid on its side, as represented in Fig. 95 a. Since he had 
shown that the electrification by contact was independent of the 
extent of the surfaces in contact, the same effect would be pro- 
duced if the copper and zinc pairs were separated and touched 
only at the top as shown in b. Being spread apart in this way, 



152 



ELEMENTS OF ELECTRICITY. 



glass cups, represented by the dotted lines, could be slipped under 
the pairs which were separated by the moistened cloth, the cloth 
could then be withdrawn, and the cups filled with the liquid itself. 
This modified form very quickly displaced the original pile. The 
individual cups are designated cells, and a series of two or more 
is called a battery, the primary meaning of the word battery being 



u 



I 



I J 



I LI 



'-' I ±L> L 



a Fig. 95. b 

a number of similar utensils placed side by side. For use with 
these batteries, the zinc-copper pairs were in the form of a strip 
joined at the middle and bent into the arc of a circle so as to be 
inserted into the cups. This is the origin of such terms as "con- 
nected in multiple arc" applied to certain groupings of cells to be 
described later. An arrangement of cells in a circle by which the 




Fig. 96. 

positive and negative ends of the battery could, for convenience, 
be brought close together (Fig. 96), was called by Volta his "cour- 
onne de tasses" or circlet of cups. 

192. Source of Electrical Energy in a Cell. — It will have been 
noted that in Par. 188 the statement was made that no current 
could be produced by the contact of dissimilar metals, yet Volta, 
proceeding on the contrary assumption devised the pile and the 
battery, both of which produce a continuous supply of electricity. 



VOLTAIC ELECTRICITY. 153 

In Par. 189 we saw that when zinc and copper are brought to- 
gether in air, the metals, being good conductors, come to a common 
potential and the air surrounding the zinc is left at a higher 
potential than that around the copper. When, however, these 
metals are immersed in a chemically active liquid, a different state 
of affairs results, for in this case the medium surrounding the 
metals, instead of being a non-conductor like the air, is a con- 
ductor and hence at a uniform potential. We also saw (Par. 187) 
that when a metal is attacked by a liquid, an electro-motive force 
is set up from the metal towards the liquid. In this case, the zinc 
being the more vigorously attacked, the electro-motive force 
acting from the zinc is greater than that acting from the copper; 
positive electricity is therefore driven across from the zinc to the 
copper and the zinc itself is left negatively charged. The copper 
is, therefore, at a higher potential than the zinc and if it be con- 
nected to the zinc by a wire, a current will flow through this wire 
from the copper to the zinc. The source of the electrical energy 
in these arrangements is not at the junction of the two metals but 
at the point of contact of the zinc with the brine or the dilute 
acid and is due to the chemical action which there takes place. 
For this reason, the left hand copper strip and the right hand zinc 
strip in Fig. 95 b can be omitted, as shown in Fig. 96, without 
affecting the strength of the battery. See also Pars. 217 and 279. 



154 



ELEMENTS OF ELECTRICITY. 



CHAPTER 19, 



THE SIMPLE CELL. 



COPPER 



193. Simple Voltaic Cell. — A voltaic cell in its simplest form 
consists (Fig. 97) of a glass cup partly filled with acidulated water, 
called the electrolyte, into which dip a strip of copper and one of 
zinc, sometimes spoken of as the elements of the cell. We shall 

suppose that, as represented in 
Fig. 97, to each of these strips 
there is attached a wire. If the 
zinc be pure, or if it has been 
treated as will be explained later 
(Par. 197), no action will be 
observed so long as the strips 
are kept apart. If, however, 
they are inclined towards each 
other so as to touch either above 
or below the surface of the liquid, 
or if they be brought into con- 
tact indirectly by joining the ends 
of the two wires, then bubbles 
of gas will immediately appear 
on the surface of the copper and 
the zinc will be observed to dissolve away gradually. This cor- 
rosion of the zinc and evolution of bubbles will continue only so 
long as the strips are in contact or the wires are connected, 
and during this time a current of electricity will flow through 
the liquid from the zinc to the copper and from the copper 
through the point of contact of the two strips, or through the 
connecting wire, back to the zinc. Since, until quite recently, 
the direction in which the electric current actually flows could 
not be determined, by convention and from analogy with water, 
it was agreed that it flows from the point of high potential to 
that of lower, or from positive to negative; therefore, since the 
current is due to the chemical energy developed on the surface 
of the zinc and originates there, the zinc plate is called the positive 




Fig. 97. 



VOLTAIC ELECTRICITY. 155 

plate and consequently the copper is the negative plate. The 
current crosses the liquid to the copper plate, ascends this plate 
to the attached wire, follows along the wires to the junction with 
the zinc plate and descends this plate to the point of starting. 
The points of attachment of the wires to the copper and zinc are 
called the poles of the cell, and since the current flows from the 
copper out into the connecting wire, the copper pole is called the 
positive pole, the zinc, the negative pole. On account of the con- 
fusion sometimes resulting from this nomenclature, it is perhaps 
unfortunate that the copper should be both the positive pole and 
the negative plate and that the zinc should be the positive plate 
but the negative pole. As an aid to the beginner it may be 
remembered that the positive plate is the one which is attacked 
by the electrolyte and is the point of origin of the current. 

194. Material Used for Elements of a Cell. — The elements of a 
cell are usually metal, or carbon and a metal. The farther apart 
the elements are on the list as given in Par. 187, the more vigorous 
will be the chemical action set up in the cell and consequently the 
greater the electrical energy developed. The positive plate should 
be of the metal most freely attacked by the electrolyte; the nega- 
tive plate should be of the metal attacked least. The alkaline 
and the alkaline-earth metals head the list but decompose water 
and combine with acids with almost explosive violence ; they are, 
therefore, unfitted for use. The most suitable metal for the posi- 
tive plate, both from the standpoint of chemical action and of 
cost, is zinc, while carbon, copper and platinum are the substances 
most frequently used as negative plates. 

195. Chemical Action in a Simple Cell.— If the electrolyte of 
the simple cell be dilute sulphuric acid, the chemical action when 
the circuit is closed is in accordance with the following reaction: 

Zn+H 2 S0 4 = ZnS0 4 + H 2 

The zinc sulphate passes into solution as it is formed and the 
hydrogen is evolved as bubbles at the surface of the copper plate. 
Since the chemical action takes place at the surface of the zinc, 
it would seem that the hydrogen bubbles should be released at that 
point or else that they should be seen passing through the liquid 
to reach the copper plate. The reason why neither of these occur 
is explained in Par. 274. 



156 ELEMENTS OF ELECTRICITY. 

If the hydrogen be collected under an inverted jar and its weight 
be determined, and if the zinc plate be weighed at the beginning 
and conclusion of the experiment, it is found that while two parts 
of hydrogen are being produced, 65 parts of zinc are eaten away, 
that is, chemically equivalent amounts of the two are evolved 
and dissolved respectively, or the action is strictly chemical. 

Instead of dilute acid a saline solution is often used as an electro- 
lyte, ammonium chloride being frequently employed. The reac- 
tion in this case is 

Zn +2NH 4 C1 = ZnCl 2 +2NH 3 +H 2 

both the zinc chlo- 
ride and the ammonia passing into solution. 

196. Local Action. — In Par. 193 it was stated that if a plate of 
pure zinc be dipped into dilute sulphuric acid, no effect would be 
produced. Commercial zinc, however, is far from being pure and 
contains appreciable amounts of iron, lead and other substances. 
If such a plate be dipped into the electrolyte, chemical action 
immediately ensues, bubbles of hydrogen gas are evolved, the plate 
becomes pitted and may eventually be eaten through, and the 
acid becomes spent. The explanation is that the minute particles 
of the foreign metal in contact with the zinc constitute tiny voltaic 
pairs, local currents set up from the zinc through the electrolyte 
to the particles and back to the zinc, and cup-shaped depressions 
are eaten out around these particles until the latter become dis- 
engaged and fall. This process is called local action. The currents 
produced are parasitic and wasteful, existing at the expense of the 
materials of the cell but contributing nothing to its useful energy. 

The rapid rusting of a nickel-plated piece of iron, once that the 
nickel coating is cut through, and the corrosion about the heads of 
iron nails driven through the copper sheathing of vessels is similar 
to this local action., 

197. Remedy for Local Action. — The logical remedy for local 
action would be the use of chemically pure zinc but the cost 
renders this prohibitive. However, in 1830 it was discovered that 
local action can be almost entirely obviated if the surface of the 
zinc be amalgamated, that is, covered with a thin layer of mercury. 
This may be done either by adding about four per cent of mercury 
to the zinc at the time when it is cast into plates, or by cleaning 
the surface by dilute acid and then rubbing mercury upon it with 
a bit of rag. The mercury unites with the zinc forming a sort of 



VOLTAIC ELECTRICITY. 157 

silvery paste but does not dissolve the particles of iron which are 
either covered up or else float to the surface of the amalgam and 
drop off. As the zinc in the amalgam is eaten away during use of 
the cell, the mercury amalgamates new layers of the zinc beneath. 
The action of the amalgam is explained thus. If local action die! 
set up between zinc and mercury, hydrogen would be released on 
the surface of the latter, just as it is on the copper plate of a zinc- 
copper couple. Mercury is known to resist the deposition of 
hydrogen, possibly because of its very smooth surface. Platinum 
with a polished surface is known to resist the deposition of hy- 
drogen much more than when its surface is rough. 

198. Polarization. — If the wires attached to the poles of a simple 
cell be brought into contact, a current will immediately flow 
through the circuit, but if it be measured by any of the means to 
be described later, this current will be found to fall off rapidly. 
If the copper plate be observed, it will be noted that not all of the 
hydrogen bubbles released at this plate rise to the top but many 
remain adhering to it and the surface of the plate rapidly acquires 
a silvery bloom. The negative plate is then said to be polarized. 
It is this layer of hydrogen which causes the current to dwindle 
and it does so in two ways, one mechanical, the other electro- 
chemical. First, the hydrogen being a non-conductor, each bubble 
in contact with the copper withdraws just so much of the surface 
of this plate from contact with the liquid and diminishes by just 
so much the cross-section of the path available for the passage of 
the current. It therefore cuts down the current by putting resist- 
ance in its path. Second, the film of bubbles upon the plate causes 
it to approximate in behavior to a plate of hydrogen, and since 
hydrogen has a greater tendency to oxidize than has copper, the 
effect is to set up a greater electro-motive force opposed in direc- 
tion to that from the zinc. We have seen (Par. 192) that it was the 
difference between the electro-motive forces acting from the zinc 
and from the copper which drove the current through the cell, 
consequently, when this difference becomes smaller, the current 
also becomes smaller. 

This diminution of the current by polarization may be avoided 
by surrounding the negative plate by some agent, either solid or 
liquid, which will oxidize the hydrogen, converting it into water, 
or will enter into combination with it, releasing in its stead some 
element which does not increase the resistance of the negative 



158 ELEMENTS OF ELECTRICITY. 

plate. The endeavor to do away with this polarization is largely 
responsible for the different varieties of cells described in the fol- 
lowing chapter. 

199. Depolarizers. — Among the many substances which have 
been employed for this oxidation of the hydrogen are the liquids 
nitric acid, solutions of nitrate of potassium, of the bichromates 
of potassium and sodium, of ferric chloride, etc., and the solids 
black oxide of manganese, peroxide of lead, and oxide of copper. 
The solid depolarizers may be made into a pasty mass and moulded 
about the negative plate or may be made into briquettes and 
fastened to the negative plate by rubber bands. The liquid de- 
polarizers may sometimes be mixed with the electrolyte but in 
most cases would attack the positive plate, even when the circuit 
was open, therefore, to prevent their reaching the positive plate 
but at the same time not to hinder the passage of the current, 
they are usually put along with the negative plate in an interior 
unglazed and porous porcelain cup which is placed in the electro- 
lyte. Such cells are sometimes called two-fluid cells. 

200. Requirements of a Voltaic Cell. — The properties desired in 
a good primary cell are the following: 

(1) It should have a high and constant electro-motive force, 

preferably greater than one volt. 

(2) It should have low internal resistance. 

(3) It should give a constant current and should, therefore, be 

free from polarization. 

(4) It should be free from local action, its elements not being 

consumed except when it is supplying current. 

(5) Its elements should be cheap. The cost of plates of gold, 

platinum or silver is in most cases prohibitive. 

(6) Its elements should be durable, not requiring too frequent 

renewal or too much attention. 

(7) It should not emit corrosive or poisonous fumes. 

(8) The electrolyte should not freeze readily. 

No cell has yet been devised which fulfills all of these conditions, 
and for different uses they are not equally important. For example, 
constancy of current, while essential when a small electrical ma- 
chine, such as a fan, is to be run, is not so where the cells are used 
intermittently and then only for very brief periods, as is the case 



VOLTAIC ELECTRICITY. 159 

with those that operate door and call bells. Again, for telegraphy 
over a long line of considerable resistance, a moderate internal 
resistance of the cell is not very objectionable. 

The E. M. F. of a cell is independent of the size of its plates or 
of the depth to which they are immersed in the electrolyte, that is, 
of the size of the cell, but depends entirely upon the relative posi- 
tion of its elements in Volta's series (Par. 187). The E. M. F. of 
a zinc-copper-sulphuric acid cell is the same whether the cell be as 
large as a barrel or as small as a thimble. Therefore, the elements 
of a cell having been selected, its E. M. F. is fixed. The quantity 
of electricity produced varies, however, with the amount of chemi- 
cal action in the cell and this varies directly with the size of the 
plates. 



160 ELEMENTS OF ELECTRICITY. 



CHAPTER 20. 

KINDS OF CELLS. 

201. Great Variety of Cells.— Any two conducting substances 
which dip into a vessel containing a liquid which attacks one more 
than it does the other, constitute a primary cell, also called a voltaic 
or a galvanic cell. There are, therefore, a great many possible 
arrangements by which electricity may be generated by chemical 
means and this number is still further increased when we consider 
the many expedients adopted for avoiding polarization. It would 
therefore seem that the number of kinds of cells would be limited 
only by the ingenuity of the inventor and such would be the case 
were it not for the required conditions (Par. 200) which not being 
fulfilled by the majority of the possible combinations cause these 
combinations to be rejected. Notwithstanding this, the variety 
is still great and the few described in the following pages must 
be regarded as types of general classes. 

202. Classification of Cells. — Cells may be divided into two 
general classes, primary and secondary. The primary cell has 
been defined above (Par. 201) ; the secondary cell differs from the 
primary mainly in that when it has become exhausted, an electric 
current may be passed through it in a contrary direction to the 
current which it supplied, the chemical changes which have taken 
place may be undone and the cell can be restored to its primitive 
condition. It is therefore analogous to a clock which, when run 
down, can be wound up again. Secondary cells are used in storage 
batteries and will be considered in detail when we reach that subject 
(Chapter 22). 

Primary cells are of two classes, those without depolarizers 
(such as the simple cell described in Par. 193), and those with 
depolarizers. This latter class may be subdivided according as 
the depolarizer is a liquid or a solid. Other subdivisions may be 
made, as, for example, single-fluid cells, two-fluid cells, dry cells, 
standard cells, etc., but this classification is not of sufficient im- 
portance to be dwelt upon longer. 



VOLTAIC ELECTRICITY. 



161 



203. Grove's Cell. — One of the first cells in which a chemical 
depolarizer was employed was invented by Grove in 1839. This 
consists (Fig. 98) of a flattened, rectangular outer cell A of glass 
or of vulcanized rubber, containing dilute 
sulphuric acid into which dips the U-shaped 
amalgamated zinc plate B. Within the 
loop of this zinc plate there fits a flat porous 
cell C containing concentrated nitric acid 
and the platinum negative plate D. The 
hydrogen produced by the action in the 
external cell is attacked by the nitric acid 
as follows: 

3H+HN0 3 = 2H 2 0+NO 




Fig. 98. 



The nitric oxide, NO, produces no polar- 
ization since it either dissolves in the acid 
or escapes into the air where, in contact with 
oxygen, it becomes nitric peroxide, N0 2 , a 
reddish brown, irritating gas. The cell has a high electro-motive 
force, very nearly two volts, and owing to the great amount of 
surface of the zinc plate and the short 
distance from the zinc to the platinum 
plate, it has small internal resistance. The 
objections to this cell are the corro- 
sive and poisonous character of the nitric 
peroxide fumes and the cost of the plati- 
num plates. These last need be no thicker 
than tin-foil, but since the cost of plati- 
num is now very much more than that 
of gold, they are necessarily very expen- 
sive. 




fcA 



204. The Bunsen Cell. — To avoid the 
expense of the platinum plate, Bunsen, in 
the year following the invention of the 
Grove cell, suggested the use in its stead 
of a plate of hard carbon. These plates 
are prepared from gas coke or that par- 
ticular hard and semi-metallic form of carbon resulting from the 
decomposition by heat of gaseous hydro-carbons and occurring 
as a deposit in the retorts and flues of gas works. The principle 



Fig. 99. 



162 



ELEMENTS OF ELECTRICITY. 



of the Bunsen cell is precisely the same as that of Grove's cell. 
The carbon plate (C, Fig. 99) is in shape a square prism and dips 
into nitric acid in an inner porous cup. The zinc plate Z is a 
split cylinder and embraces this inner cup. The cell gives off the 
same corrosive fumes as the Grove cell but the greatest objection 
to it is the difficulty of making electrical connection with the 
carbon plate. This plate being porous, it is difficult to attach 
wires to it directly. To remedy this, the upper end of the plate 
is sometimes copper plated, after which the connector is clamped 
to it as shown in Fig. 99. Also, owing to its porosity, the plate 
soaks up the nitric acid which, upon rising to the height of the 
copper plating or of the connecting wires, will corrode the con- 
nections. This is partly remedied by soaking the upper end of 
the plate in melted paraffine which, being impervious to the acid, 
hinders its rise. 

205. The Bichromate Cell. — There are a number of cells which 
instead of nitric acid employ either chromic acid or the bichro- 
mates of potassium or of sodium as depolarizers, but are otherwise 

the same as the Bunsen cell. It is found 
that in these the inner porous cell is not 
necessary and the bichromate solution 
may be allowed to mingle freely with the 
sulphuric acid, in fact, they are sold ready 
mixed under the name electropoion fluid. 
The hydrogen released by the action of 
the sulphuric acid upon the zinc is oxi- 
dized by the bichromate, the products 
being water and chrome alum thus 

K 2 Cr 2 7 + 4H 2 S0 4 + 6H = 
2KCr(S0 4 )2+7H 2 

206. Darnell's Cell. — The first cell to 
avoid polarization was invented by Daniell 
in 1836 and, although using a liquid de- 
polarizer, the principle of its action is quite 
different from that of the cells described 
in the preceding paragraphs. Fig. 100 
represents one of its many forms. This consists of an inner 
porous cup, which contains dilute sulphuric acid, and the zinc 
plate. The zinc is given the corrugated form shown in the figure 




Fig. 100. 



VOLTAIC ELECTRICITY. 163 

in order to expose more surface to the action of the acid. The 
copper plate, in the form of a split cylinder, surrounds the inner 
cup and is immersed in a solution of copper sulphate contained 
in the outer cell. As it is important that this last solution should 
be kept saturated, there is fastened to the side of the copper plate 
a little cup or shelf with perforated bottom and this cup is kept 
filled with crystals of copper sulphate. 

The chemical action in the inner cell is the same as already 
described but the hydrogen on coming in contact with the copper 
sulphate solution displaces the copper and takes its place and 
the copper is deposited on the negative plate thus 

H 2 + CuS0 4 = H 2 S0 4 +Cu 

There is, therefore, no polarization and the copper plate simply 
grows thicker by the deposition upon its surface of successive films 
of copper. The copper sulphate solution would, however, become 
gradually exhausted were it not continually replenished from the 
crystals on the perforated shelf. 

The sulphuric acid in the inner cup is gradually converted to a 
solution of zinc sulphate but the cell continues to operate, in fact, 
the inner cup is often filled from the beginning with a solution of 
zinc sulphate. In this case the following reaction takes place: 

ZnS0 4 +CuS0 4 = S0 4 +ZnS0 4 +Cu 

the copper being deposited upon the negative plate as before and 
the sulphion, S0 4 , attacking fresh portions of the zinc and again 
becoming zinc sulphate. 

The electro-motive force of a Daniell cell averages about 1.0.7 
volts but fluctuates slightly with the variation in the strength 
of the two solutions and also with the temperature. Being free 
from polarization, it is very largely used where constant currents 
are required, as is especially the case in telegraphy in this country. 

207. Gravity Cell. — A saturated solution of copper sulphate 
has a specific gravity of about 1.20 and if the specific gravity" of 
the zinc sulphate solution be kept below this figure, it is possible 
to do away with the inner cup of the Daniell cell and to separate 
the two fluids by the difference in their densities. Such a cell, 
called a gravity cell, is represented in Fig. 101. The copper plate, 
of the shape shown, is placed upon the bottom of the cell and 
the copper sulphate solution with extra crystals is poured over it. 
The wire from this plate is protected by rubber or by a glass 



164 



ELEMENTS OF ELECTRICITY. 




Fig. 101. 



tube up to the top of the cell. The zinc plate, of the shape shown, 

is hung from the edge of the cell and is covered with a dilute 

solution of zinc sulphate. As the cell is 
used the zinc sulphate solution increases 
in density. It must therefore be tested 
from time to time by means of a hydrom- 
eter (a little graduated glass float which 
stands higher in the liquid as the latter 
grows denser, and sinks lower as it grows 
less dense), and should the density reach 
1.15, a portion of the solution must be 
drawn off by a syringe or a siphon and 
water added in its place. If the cell be 
unused for some time, the two fluids will 
mingle by diffusion and when the copper 
sulphate solution reaches the zinc plate, 
metallic copper will be deposited upon 
this plate with the result that local action 
will ensue. 
From the shape of the zinc plate, these cells are commonly 

known as crowfoot batteries. 

208. The Edison-Lalande Cell.- 

employing a solid depolarizer. It 

positive plates of zinc bolted together at the 

top and arranged one on either side of the 

negative plate. This last is of cupric oxide 

compressed into the required shape and size. 

During the process there is added some 

cementing material which when heated binds 

the particles firmly together. The com- 
pleted plate is inserted in a copper frame by 

which it is suspended from the lid of the cell. 

The arrangement is shown in Fig. 102 in 

which, for the sake of clearness, one of the 

zinc plates has been omitted. The electrolyte 

is a solution of caustic potash (potassium 

hydroxide) which when the circuit is closed attacks the zinc, pro- 
ducing a double oxide of zinc and potassium (potassium zincate) 

and releasing hydrogen, thus 

Zn +2KOH = K 2 Zn0 2 +H 2 



This is an example of a cell 
has two 




VOLTAIC ELECTRICITY. 



165 



The hydrogen reduces the copper oxide of the negative plate as 

follows : 

H 2 +CuO = H 2 0+Cu 

and there is therefore 
no polarization. 

The electro-motive force of these cells is low (only .7 volt), but 
the internal resistance is very small and their efficiency is high. 

Potassium hydroxide has a great affinity for carbon dioxide and 
will absorb this gas from the air, becoming potassium carbonate. 
To prevent this, a layer of heavy paraffine oil must be poured upon 
the surface of the electrolyte. 

209. The Leclanche Cell.— The Leclanche cell, invented in 1868, 
also uses a solid depolarizer. From its cheapness, simplicity and 
freedom from dangerous chemicals it 
is extremely popular and in one form 
or another is probably more used than 
all other kinds combined. A common 
form is shown in Fig. 103. The cell is 
generally a glass jar, the positive ele- 
ment an amalgamated zinc rod placed 
in one corner of the jar, and the nega- 
tive plate is of gas carbon. The depolar- 
izer is manganese dioxide used in the 
form of a black powder and the many 
forms of this cell found upon the market 
are based mainly on differences in the 
method of applying the depolarizer to 
the carbon plate. In the original cell 
the carbon plate was placed in a porous 
cup which was then packed with the 

powdered depolarizer. In modern forms the dioxide may be 
cemented about the carbon plate, or made into briquettes and 
fastened to this plate by rubber bands, or may even be com- 
pounded with the carbon plate itself. Since the dioxide is a poor 
conductor, when it entirely surrounds the carbon plate it is always 
mixed with powdered carbon by which its resistance is reduced. 
The electrolyte is a solution of sal ammoniac (ammonium chloride) 
and the reaction when the circuit is closed is 




Fie. 103. 



Zn +2NH 4 C1 = ZnCl 2 +2NH 3 + H, 



166 



ELEMENTS OF ELECTRICITY. 



The action of the depolarizer is 

H 2 +2Mn0 2 = H 2 + Mn 2 3 

Since chemical action is much retarded when one of the reagents 
is in the form of a solid, the depolarization in a Leclanche cell does 
not take place quickly enough to consume the hydrogen as fast as 
it forms and the cell polarizes rapidly. However, as the chemical 
action, oxidizing of the hydrogen, keeps on steadily after the cir- 
cuit is broken, the cell will recover after a short rest. These cells 
are, therefore, not fitted to supply a continuous current but are 
admirably adapted for intermittent use as in telephones, door 
bells, etc. Their electro-motive force is about 1.4 volts, there is 
no local action and they require a minimum amount of attention. 

210. Dry Cells. — The so-called dry cells, in common use in this 
country, are in principle simply Leclanche cells in which the liquid 
has been reduced to a minimum. A cross-section 
of one of these cells is shown in Fig. 104. The 
cell proper is a zinc can which serves both as the 
cell and as the positive plate. The negative 
plate is of gas carbon and may be corrugated or 
fluted so as to expose more surface. It is placed 
in the can and packed around with a mixture of 
manganese dioxide and granular coke. The 
packing is then saturated with electrolyte, usu- 
ally a solution of zinc chloride and ammonium 
chloride, after which the cell is sealed with a 
layer of pitch or asphalt. This serves a double 
purpose; it holds the carbon plate rigidly in 
position and it prevents the evaporation of the 
electrolyte. To secure the seal more firmly a 
cannelure or groove is made around the cell near the top. In 
some of these cells a cementing material is mixed with the de- 
polarizer; in others the can is lined with asbestus or with paste- 
board which has been soaked with the electrolyte. For insulation, 
the cell is usually placed in an outer box of pasteboard. 

For many purposes these dry cells have entirely superseded the 
wet cells. They are very cheap, costing now less than 20 cents 
apiece, and for average door-bell use should last from two to three 
years. If the asphalt seal becomes cracked, they soon dry out and 
cease to act. 




VOLTAIC ELECTRICITY. 167 

211. Need of Standard Cells. — One of the most important 
classes of measurements with which the electrician has to deal is 
that of electro-motive force. In Chapter 11 we examined electrom- 
eters, a form of apparatus sometimes used for this purpose, and 
in Chapter 34 we shall describe voltmeters, instruments better 
adapted for practical use since they are arranged so that the elec- 
tro-motive force which is being measured can be read direct from 
a printed scale without the necessity of resorting to intermediate 
calculations. Even the best instruments, however, do occasion- 
ally get out of adjustment and it is very desirable that we should 
possess standards of electro-motive force by which our instru- 
ments can be calibrated in the first place and compared and checked 
in the second. While the average E. M. F. of the cells described 
in the preceding paragraphs can be stated with considerable 
accuracy, the actual E. M. F. is dependent upon varying conditions 
and, between limits, fluctuates too irregularly and with too much 
uncertainty for these cells to be used as standards. However, 
there have been devised certain "standard cells" in which the 
variable factors, except that of temperature, have been eliminated 
and the temperature coefficient, or change of E. M. F. with tem- 
perature, determined. These cells are used for their E. M. F. and 
not to supply current and since the E. M. F. is independent of the 
size of the cells (Par. 200), they are made very small, some, in fact, 
being hardly larger than a thimble. Analogous to this would be 
the use of vertical columns of water as standards of pressure. 
Since hydrostatic pressure per unit area is dependent upon the 
height of the column and is independent of its cross-section, and 
since no current or flow of water is required, these vertical columns 
could be contained in slender tubes. 

212. Clark's Standard Cell.— In 1893 the International Con- 
gress of Electricians in session in Chicago passed resolutions defin- 
ing certain electrical units upon which at that time the scientific 
world was not universally agreed. These definitions were formally 
legalized by Act of Congress, approved July 12, 1894. Among 
others, there was defined the unit of electro-motive force, the inter- 
national volt, and to the definition proper was added that it was 
"represented sufficiently well for practical use by Hf^ of the elec- 
tro-motive force between the poles of the voltaic cell, known as 
Clark's cell, at a temperature of 15° C and prepared in the manner 
described in the accompanying specification." 



168 



ELEMENTS OF ELECTRICITY. 



There are a number of forms of this cell. The one shown in Fig. 
105 is in accordance with the specification referred to. The cell 
proper is a two-limbed bottle closed with a ground-glass stopper. 
Through the bottom of each limb there is fused a fine platinum 
wire, the two serving as the terminals of the cell. In principle, 

the cell is the same as DanielFs. 
The positive plate is amalgamated 
zinc, the negative plate is mercury, 
the electrolyte is a solution of zinc 
sulphate and the depolarizer is 
mercurous sulphate. The zinc a- 
malgam is composed of nine parts 
of mercury and one of zinc, and is 
liquid at the temperature of boil- 
ing water but sets at ordinary 
temperatures. It is melted and 
poured into one of the limbs. 
Upon this is packed a half-inch 
layer of crystals of zinc sulphate. 
In the other limb is poured per- 
fectly pure mercury, then on top 
of this a layer of mercurous and 
zinc sulphates worked up together 
into a paste, and on top of this paste a half-inch layer of the 
crystals of zinc sulphate. Finally, the bottle is filled to the neck 
with a saturated solution of zinc sulphate and the stopper is 
cemented in with shellac, leaving beneath it a small air bubble to 
allow for expansion of the liquid with changes of temperature. 
The cell is then placed in a protecting outer case, the wires being 
brought out to suitable binding posts, and an opening is left in the 
cover through which a thermometer may be inserted to take the 
temperature of the cell. 

The chemical action is similar to that given for DanielFs cell 
(Par. 206). 

ZnS0 4 +Hg 2 S04 = S04+ZnS0 4 +Hg 2 




V«cAmiA*V# 



Fig. 105. 



the SO 4 attacking 
the zinc of the positive plate, the Hg 2 coalescing with the mercury 
of the negative plate and there thus being no polarization. 

The E. M. F. of a Clark cell at 15° C (59° F) is 1.434 volts and 



VOLTAIC ELECTRICITY. 169 

its temperature coefficient or change of E. M. F. per degree Centi- 
grade is about .00115. This is negative, that is, the E. M. F. 
decreases as the temperature increases. At 50° F it is 1.440; at 
80° F it is 1.421. This change in E. M. F. with change in tempera- 
ture is due to corresponding change in solubility of zinc sulphate 
and hence variation in the density of the electrolyte. The exact 
E. M. F.*at any temperature t Centigrade is given by the formula 

E; = 1.434 - .00119 (t - 15) - .000007 (i - 15) 2 

213. Weston's Standard Cell.— The Weston standard cell is 
in principle precisely the same as the Clark cell, cadmium being 
substituted for zinc, that is, the positive plate being a cadmium 
amalgam, the electrolyte being a saturated solution of cadmium 
sulphate, etc., and the mechanical arrangement being similar to 
that just described. Since the solubility of cadmium sulphate 
varies but little with temperature, the temperature coefficient is 
very small, being only .00004 volt per degree Centigrade. For all 
ordinary purposes, this change may be 
neglected and the E. M. F. of the cell 
may be taken as 1.019 volts. 

214. Conventional Sign for Cell. — 
Since in the study of electricity it often 
becomes necessary to make diagrams in ■ ■ 

which cells appear, a conventional sign 1| | I 

for the same has been adopted. In Fig. I 

106, a represents the plan of two cells b 

connected together and b represents the Fi 106 

conventional sign for the same two cells. 

In both, the short heavy line represents the zinc, the long thin 
line the copper. It will be noted that in the conventional sign 
the cell itself is omitted as well as the connecting wire between 
the cells. 




170 ELEMENTS OF ELECTRICITY. 



CHAPTEK 21. 

THE ELECTRIC CURRENT AND ITS CHEMICAL 

ACTION. 

215. Electric Current. — In Par. 70 it was stated that when 
conductors at different potentials are brought into contact (either 
directly or through a third conducting body), there is a flow of 
positive electricity from the one of higher potential to that of 
lower. Again, in Par. 75 it was stated that if new charges were 
supplied to the body of higher potential as fast as the preceding 
charges flowed away, then the body would be maintained at a 
constant potential and the successive charges flowing away 
would constitute a continuous stream or current. Such is the 
state of affairs in a voltaic cell. The chemical action at the surface 
of the zinc plate produces fresh quantities of electricity as fast as 
those previously produced flow away. These successive charges 
pass across to the copper plate and raise its potential, and if this 
copper plate be connected by a wire to the zinc plate a current 
will flow through the wire. Under these conditions, certain 
perceptible effects are produced along the conductor; among 
them (a) the temperature of the conductor rises, (b) a magnetic 
field is established about the conductor and (c) if a part of the 
conducting path lies through a chemical compound, chemical 
decomposition will generally ensue. We are agreed then that 
when these phenomena occur, a current is flowing through the 
conductor. The terms "current," "flow," etc., are survivors of 
the time when electricity was spoken of and regarded as a fluid, 
and being such convenient forms of expression they are retained. 

216. No Current Unless Circuit be Complete. — The path over 
which the current flows is called the circuit. There can be no flow 
unless this circuit be complete, that is, unless there be a continuous 
conducting path from the surface at which the current originates 
back to the other side of this surface. If the circuit be continu- 
ous it is said to be broken or open. Since the current thus returns 
upon itself, it is analogous to water which entirely fills a pipe bent 



VOLTAIC ELECTRICITY. 171 

around into the form of a ring. If this water be put in motion it 
can be checked by closing a cock in the pipe at any point whatso- 
ever. So the electric current is stopped by breaking the circuit at 
any point at all. 

217. Direction of Flow of Current. — According to the Elec- 
tron Theory, certain of the electrons may oe detached from their 
little atomic systems and may wander about from one system to 
another. These free electrons are especially abundant in con- 
ductors but are almost lacking in non-conductors, indeed, it is 
their presence or absence which determines whether a body is to 
be classed as a conductor or as a non-conductor. Should a 
difference of potential be established between two points of a 
conductor, the movements of the electrons, which up to that time 
had been haphazard, immediately become ordered, and, since 
they all carry negative charges, they move from negative to 
positive. It is their movement which constitutes the electric 
current. It is therefore seen that our previous assumption that 
the electric current consists of positive charges moving from high 
potential to low is incorrect. We are, however, forced to adhere 
to this because all the vast numbers of electrical machines, appa- 
ratus, instruments, batteries, etc., are designed, arranged for 
connection and marked in accordance with the first assumption 
and should the attempt now be made to correct this, the con- 
fusion resulting would be in the nature of a catastrophe. More- 
over, a current consisting of negative charges moving in a negative 
direction is equivalent to a positive current in the opposite direc- 
tion and our mathematical conclusions are not upset. (Par. 674.) 

Some of the phenomena produced by the current do have 
direction with respect to the assumed direction of flow. The 
heating effect of the current in a homogeneous conductor is 
irrespective of the direction of flow, but the direction of the 
magnetic field about the conductor and the direction in which 
the products of electro-chemical decomposition move are depen- 
dent upon this flow and are reversed whea the direction of the 
current is reversed. 

218. Decomposition of Water.— On March 20, 1800, Volta 
addressed to Sir Joseph Banks of the Royal Society of London a 
portion of a letter describing the Voltaic Pile. This letter was not 
communicated to the Society until some time in June when the 
remainder had been received, but in the mean time it had been 



172 



ELEMENTS OF ELECTRICITY. 




shown to two of the members, Carlisle and Nicholson. Wishing 
to test the apparatus, they extemporized one with seventeen silver 
coins, an equal number of copper discs and pieces of cloth soaked 
in a weak solution of common salt. In order to make good con- 
nection with a metal plate which they were endeavoring to charge, 
they placed upon it a drop of water and inserted in this drop the 
end of one of the wires from the pile. At once fine bubbles rose 
in the liquid. Continuing these investigations, Nicholson within 
the next few days devised another experiment. He inserted in 
one end of a glass tube a cork, poured some water into the tube 
and then corked the other end. Through each of these corks he 
then thrust a platinum wire so that the ends protruded some dis- 
tance into the water. When these wires were 
connected to the extremities of the pile, streams 
of bubbles were given off from each of the ends, 
and when tested separately, it was found that 
oxygen was released at the wire by which the 
current entered the water and hydrogen at the 
wire by which it left. 

219. Electrolysis of Water. — This decompo- 
sition produced by the electric current is called 
"electrolysis," i. e., electric analysis. The elec- 
trolysis of water can best be studied by means 
of the apparatus shown in Fig. 107. This con- 
sists of three glass tubes connected as shown. 
The tubes H and are burettes graduated in 
cubic centimeters, usually to the nearest tenth, 
the graduations reading from the top down- 
ward. Through the bottom of these burettes 
there are sealed the platinum wires A and B 
terminating on the inside in the platinum plates 
C and D. The third tube is expanded at the 
top into the reservoir R which is at a higher 
level than the tips of the burettes. The apparatus is supported 
on a suitable stand. With the stop cocks H and open, water, 
to which a few drops of sulphuric acid have been added, is poured 
into R. The liquid rises in the burettes and the stop cocks are 
closed as soon as its level passes them. The addition of the 
sulphuric acid is usually explained by the statement that it is 
used merely to improve the conducting power of the water. 




Fig. 107. 



VOLTAIC ELECTRICITY. 173 

Perfectly pure water is a non-conductor, and the acidulated 
water does conduct, but the true reason for the use of the acid 
is given below. If a current be now brought in at A and out 
at B, bubbles will rise from the plates C and D and collect in 
the upper parts of the burettes, pushing down the liquid which 
will rise in the reservoir. The gas in will be found to be oxygen 
and that in H, hydrogen; furthermore, the amount of gas generated 
in H will be very nearly twice that generated in 0. The volume 
of the hydrogen would be exactly twice that of the oxygen were 
it not for the facts that (a) some of the oxygen is given off in the 
denser form of ozone, (b) some of each gas, but not proportional 
amounts, is dissolved in the water, (c) a portion of the gases is oc- 
cluded by the platinum plates and (d) owing to the difference of the 
levels of the water in the two burettes, the hydrogen is under 
greater hydrostatic pressure than is the oxygen. 

The chemical action is usually explained by saying that the 
water is decomposed into its component gases hydrogen and 
oxygen, and this is correct but it is not the primary reaction which 
takes place. The sulphuric acid is first separated into H 2 and S0 4 , 
the hydrogen being released and the S0 4 then attacking the water, 
thus 

S0 4 +H 2 0=H 2 S0 4 +0 

so that the oxygen is 
released as the result of a secondary reaction. 

220. Faraday's Terminology. — The decomposition of chemical 
compounds by the electric current was investigated by Faraday 
to whom is due the terminology now employed. As we have 
already seen, the liquid which undergoes decomposition is called 
the electrolyte and the process itself is electrolysis. The vessel in 
which electrolysis takes place is called an electrolytic cell. The 
plates or wires which dip into the liquid and by which the current 
is brought in and taken out are termed collectively the electrodes; 
that by which the current enters is the anode; that by which it 
leaves is the cathode. The part molecules into which the substance 
being decomposed is split are, in allusion to their movement 
through the liquid, called ions (wanderers) ; those which appear at 
the anode are anions; those released at the cathode are caihions 
or kations. 

221. Substances Subject to Electrolysis. — In order that a 
substance may be electrolyzed it must fulfill the following condi- 



174 ELEMENTS OF ELECTRICITY. 

tions; it must be a compound substance; it must be a conductor; 
it must be in a liquid state, either as the result of fusion or of 
solution. Mercury and the fused metals are conducting liquids 
but being elementary bodies can not be decomposed. All other 
conducting liquids undergo electrolysis. 

222. Electrolysis of a Fused Compound. — The electrolysis of 
lead chloride may be taken as an example of the decomposition 
of a fused compound. The salt is kept in a molten state in a small 
porcelain crucible placed over a bunsen burner. The electrodes 
of iron dip into the fused mass. When a current passes, chlorine 
is liberated at the anode, as may be shown by the bleaching effect 
upon a piece of litmus paper held just above, and lead is released 
at the cathode. 

223. Electrolysis of a Base. — In many cases of electrolysis the 
primary reactions are obscured by the secondary. In the elec- 
trolysis of water (Par. 219), it is really the sulphuric acid that is 
electrolyzed, the decomposition of the water being the result of 
secondary reactions. Similar results follow the electrolysis of the 
strong bases. For example, a solution of potassium hydroxide 
electrolyzes as follows: 

2KOH = K 2 +H 2 0+0 

the oxygen appearing 
at the anode and the potassium being released at the cathode, but 
as soon as this metal is released it attacks the water, thus 

K 2 +2H 2 0=2KOH+H 2 

so that the net 
result is the same as when sulphuric acid is electrolyzed, that is, 
the water is decomposed. If, however, the cathode be of mercury, 
the potassium amalgamates with it and by distilling off the mer- 
cury from the amalgam the potassium may be separated and col- 
lected. In a somewhat similar manner to this, Davy discovered 
in October, 1807, first potassium and rapidly thereafter sodium 
and other alkaline and alkaline-earth metals. 

224. Electrolysis of a Metallic Salt. — When a metallic salt in 
solution is electrolyzed. the metal appears at the cathode, the acid 
radicle at the anode, but, as mentioned above, this primary re- 
action is frequently obscured by secondary reactions. 

In the electrolysis of an alkali oxy-salt, these secondary reactions 



VOLTAIC ELECTRICITY. 175 

occur at both anode and cathode. For example, if sodium sulphate 
be electrolyzed the sodium is released at the cathode but imme- 
diately reacts with the water releasing hydrogen. The S0 4 is 
released at the anode and, as described above, reacts with the 
water releasing oxygen. The net result therefore is simply the 
electrolysis of the water. 

If a solution of copper sulphate be electrolyzed the copper is 
deposited upon the cathode and the S0 4 is released at the anode 
where one of two effects may be produced according as the anode 
is or is not attacked by the S0 4 . If the anode be of platinum, the 
SO 4 attacks the water, forming sulphuric acid and releasing 
oxygen. If, however, the anode be of copper, the S0 4 attacks it, 
producing copper sulphate which goes into solution. As fast as 
copper is deposited upon the cathode, an equal amount is dissolved 
from the anode; the electrolyte therefore remains of constant 
strength. This is true for other metals than copper. If a salt of a 
metal be electrolyzed between electrodes of that metal, the anode 
wastes away, the cathode increases and the electrolyte remains of 
constant concentration. 

The metals, which in the above are said to be released at the 
cathode, are really deposited upon the cathode in a compact and 
tightly adhering layer. This is the basis of the important proc- 
esses of electroplating and electrotyping to be described later. 
Electrolysis has many other important applications, such as the 
electrolytic refining of copper, the manufacture of chlorine, of the 
alkaline hydroxides, of aluminum, etching on metal, photo-en- 
graving, etc. 

225. Electro- Chemical Classification of the Elements. — The 
elements have been classed according to their behaviour under 
electrolysis. . Those which move in the direction of the current and 
are released at the cathode are called electro-positive, this name 
being given because they move to the negative plate. Those which 
move against the current and appear at the anode or positive plate 
are called electro-negative. Hydrogen and the metals are electro- 
positive; the non-metals are electro-negative. It will be noted 
that in its electro-chemical behaviour hydrogen conforms to its 
purely chemical behaviour and arranges itself with the metals. 
The above classification, which is also extended to compound ions, 
is not absolute; an element in certain compounds being electro- 
positive, while in others it may be electro-negative. 



176 ELEMENTS, OF ELECTRICITY. 

226. Faraday's First Law. — It was stated above (Par. 215) that 
when an electric current is flowing there is no material substance 
in movement but there is a transfer of energy which manifests 
itself in the production of heat, of magnetic effects, and of chemical 
decomposition. It is a known fact that the same amount of chem- 
ical action always produces the same amount of energy and, con- 
versely, the same expenditure of energy in the production of 
chemical decomposition always brings about the same amount. 
The truth of this was recognized by Faraday, the first to investi- 
gate the laws of electrolysis, and was formulated by him to the 
effect that the amount of chemical action produced in an electrolytic 
cell is proportional to the quantity of electricity which flows through 
the cell. The amount of chemical action produced by the passage 
of an electric current may therefore be taken as a measure of the 
quantity transferred. 

227. Voltameters. — An electrolytic cell so made that the 
chemical action produced by the current can be accurately 
measured, and hence the current determined, is called a voltameter. 
Voltameters are arranged so that the metal (usually silver or 
copper), deposited upon the cathode may be weighed, or the 
amount of gas released may be measured and its weight calculated. 
The latter class, the gas voltameters, may collect the gases sepa- 
rately, as shown in Fig. 107, or may gather these gases in a common 
burette thereby obtaining a greater volume for measurement. 

We shall shortly see that there is another instrument, a volt- 
meter, used for quite a different purpose, the measurement of 
electro-motive force. It is unfortunate that these names are so 
much alike and the beginner must be on his guard not to confound 
the two. 

228. The Coulomb and the Ampere. — To define a current of 
water, it is not sufficient to state the amount of water which will 
flow past a certain point but we must also state the rate at which 
it flows past. So also with the electric current; we must know both 
the quantity and the rate at which this quantity is delivered. 

The practical unit of electrical quantity, the coulomb, is defined as 
that quantity of electricity which flowing through a gas volta- 
meter liberates .00001035+ of a gram of hydrogen. 

Now, a very feeble current must flow a long time to accom- 
plish the same amount of chemical work as a current of greater 



VOLTAIC ELECTRICITY. 177 

strength; on the other hand, the greater the current, the greater 
the amount of work done in a given time. We can therefore com- 
pare currents by comparing the amount of chemical work done in 
a given time. The practical unit of current, the ampere, is defined 
as that unvarying current which flowing through a gas voltameter 
liberates .00001035+ of a gram of hydrogen per second. Why this 
particular weight was selected will be explained later (Pars. 231, 
232, 450). From the foregoing, it is seen that a current of one 
ampere delivers one coulomb per second, or that if Q be the number 
of coulombs, / be the current in amperes, and t be the time in 
seconds, then 

Q=It 

This may also be written I=Q/t, whence we see that the cur- 
rent in amperes is equal to the rate at which coulombs are de- 
livered, or the number of coulombs per second. 

The unit of quantity, the coulomb, must not be confused with 
the electro-static unit of quantity as defined in Par. 56. The 
coulomb js equal to very nearly 3 X 10 9 or three billion of the elec- 
trostatic units. 

With practical experience in the Laboratory, the student will 
soon form a conception of the ampere which at first must be to 
him more or less of an abstraction. The current employed in the 
16 candle power 110 volt incandescent lamp is about one-half 
ampere. 

In solving ordinary problems given for practice, it is sufficiently 
accurate to take the amount of hydrogen released by one coulomb 
as .00001 (one one-hundred thousandth) of a gram. 

229. Equality of Current at Every Cross- Section of a Circuit. — 

At every cross-section of a circuit through which a current is 
flowing, the current is the same. This is a simple principle but 
often confuses the beginner who has a tendency to suppose that a 
current may start out of a certain strength but may be used up 
and dwindle away as it progresses around the circuit. The current 
may be compared to water which completely fills a pipe bent into 
the shape of a ring. No water can move at any point unless 
exactly the same amount moves at every other cross-section of the 
pipe. 

A corollary following directly from the above is that ike amount 
of chemical action at every cross-section of a circuit is the same. 



178 



ELEMENTS OF ELECTRICITY. 



This may be shown experimentally as follows. In Fig. 108, A 
represents a battery of Daniell cells connected one after the other, 
or in series (three are represented in the diagram but as many as 
may be necessary are used), and B, C, D, and E represent copper 
voltameters. When the key K is closed, completing the circuit, 
a current flows through the battery, through B, then divides, part 
going through C and the rest through D, then reunites, passes 
through E and back to the negative pole of the battery. Before 




Fig. 108. 



closing the key, the cathodes of the voltameters and of each of the 
Daniell cells are carefully weighed. After the current has flowed 
for a while, the key is opened, stopping the current, and the 
cathodes are removed, dried, and carefully re weighed. They are 
all found to have increased in weight, the increase being exactly 
the same in all except C and D and in these their joint increase 
being equal to the increase in each of the other cathodes. It is to 
be especially noted that the amount of chemical action is also the 
same in every one of the battery cells in series. 

230. Faraday's Second Law.— Suppose we arrange a similar 
experiment with a number of voltameters in series but each con- 
taining different compounds. Suppose one to be a gas voltameter, 
one to contain a solution of silver nitrate, one of copper sulphate, 
one of cuprous chloride and one of tin tetra-chloride. If now the 
key be closed, the same current will traverse them all. After the 
current has flowed for a while, open the key, remove and weigh 
the cathodes and measure and calculate the weight of the hydrogen 
evolved in the gas voltameter. If we take the weight of this 
hydrogen as unity we will find that 107.9 parts of silver, 31.8 parts 
of copper in the copper sulphate solution, 63.6 parts in the cuprous 
chloride solution and 29.8 parts of tin have been deposited. But 



VOLTAIC ELECTRICITY. 179 

these numbers, 107.9, 31.8, 63.6, and 29.8 are the equivalent 
weights of the corresponding elements in the respective compounds. 
(The equivalent weight of an element or of a radicle is defined as 
that weight of it which combines with or displaces or is chemically 
equal to one part by weight of hydrogen. It may be obtained by 
dividing the atomic weight of the element, or the molecular weight 
of the radicle, by the valency which it has in the compound under 
consideration.) The foregoing results are expressed in Faraday's 
second law which is to the effect that the weights of the ions of 
different substances liberated by the same quantity of electricity 
are to each other as the equivalent weights of these ions. 

231. Electro- Chemical Equivalent. — The electro-chemical equiv- 
alent of an element is the weight in grams of that element 
liberated by one coulomb. By definition (Par. 228) one coulomb 
liberates .00001035+ of a gram of hydrogen, which is therefore 
its electro-chemical equivalent. The electro-chemical equivalent 
of any other element is obtained by multiplying its equivalent 
weight by this electro-chemical equivalent of hydrogen. For 
example, for silver it is 107.93 X. 00001035+ =.001118, and for 
copper it is .000328. 

To liberate one gram of hydrogen (about four-tenths of a cubic 
foot at ordinary temperature) requires 1/. 00001035 + , or, in 
round numbers, 96,540 coulombs. This would require a current 
of one ampere to flow for nearly 27 hours. This quantity of elec- 
tricity, 96,540 coulombs, will release one gram-equivalent of any 
ion, as for example 8 grams of oxygen, 107.93 grams of silver, etc. 

From the foregoing, it is seen that to find the weight of any ion 
released by a given current in a given time, we determine the num- 
ber of coulombs and multiply this number by the electro-chemical 
equivalent of the ion. 

232. Definition of the Ampere in Terms of Silver.— For prac- 
tical purposes, because of the difficulty of handling and weighing 
a gas, it is desirable to have the ampere defined in terms of some 
solid element instead of hydrogen. Silver is found to be the most 
suitable and copper the next. In the preceding paragraph we have 
seen that the electro-chemical equivalent of silver, the weight 
deposited by one coulomb, or one ampere flowing for one second, 
is .001118 gram. The International Congress of Electricians 
of 1893 in the resolutions already referred to (Par. 212), accord- 



180 ELEMENTS OF ELECTRICITY. 

ingly defined the ampere as that unit "which is represented suf- 
ficiently well for practical use by the unvarying current which 
when passed through a solution of nitrate of silver in water, in 
accordance with the accompanying specification, deposits silver 
at the rate of .001118 gramme per second." 

233. Applications of Electrolysis, Refining of Copper. — Copper 
as it comes from the smelter may contain impurities of two kinds, 
first, objectionable substances such as arsenic, antimony, etc., 
which injure its ductility and its electrical properties and, second, 
small amounts of gold and silver which it is desirable to recover 
if possible. The impure copper is cast into slabs which are used 
as the anodes in large electrolytic tanks, the electrolyte being a 
solution of copper sulphate and the cathodes being thin sheets of 
pure copper. As the current passes, the anode is eaten away, the 
pure copper being deposited upon the cathode and the impurities 
settling as a slime to the bottom of the tank whence they are 
removed from time to time and treated according to their value. 
If the impure copper contains much gold or silver, the anodes may 
be enclosed in canvas bags which permit the free passage of the 
solution but catch the slime which falls. The copper is refined at 
the rate of about seven pounds per hour per horse-power expended. 

234. Electroplating. — The object to be plated is immersed in 
the electrolyte and serves as the cathode. In gold and silver 
plating, the anode is a plate of the desired metal and the electrolyte 
is a double cyanide of potassium and this metal. The deposits 
from these cyanides are smoother and more compact than those 
from other salts. There must be a certain relation between the 
current and the area of the surface to be plated. If the current be 
too great, the deposit is granular or coarsely crystalline and may 
not adhere. Portions of the surface which are not to be plated 
may be covered with a coating of wax or varnish. 

235. Electrotyping. — The process of electrotyping is employed 
to obtain exact reproductions of wood cuts, engraved plates, 
forms of set type, etc. The need for such reproductions is readily 
understood. If impressions be taken direct from a wood cut it 
rapidly wears away and frequently gives out when about 5000 
have been struck off. By electrotyping, a reproduction of the cut 
can be made in copper and this reproduction can be used many 
thousand times and as many others may be made as desired, the 



VOLTAIC ELECTRICITY. 181 

original cut not suffering in the slightest. Again, a great many 
million postage stamps are printed annually by the Government 
and not only must they be struck off several hundred in a sheet 
but several presses must be running at the same time. If each 
plate had to be engraved separately the cost would be tremendous 
and no two stamps on a sheet would be exactly alike. However, 
the engraver prepares a plate for a single stamp and hundreds of 
reproductions can be made and these reproductions can then be 
united in one large plate. Finally, when type have been set for a 
printed page they are withdrawn from the printer's stock. Should 
this run low, he must either purchase more or distribute those 
which have been set up, thus undoing the work. However, by 
electrotyping he can reproduce the entire page in one piece and the 
type then become available for other use. 

The process consists in pressing the cut or type to be reproduced 
into a sheet of wax or other plastic material, thus making a mould. 
The interior of this mould is then dusted with very finely powdered 
graphite or bronze by which the surface is made a conductor, and 
using this as the cathode a thin layer of copper is deposited upon 
it. This thin layer is then backed by pouring into it melted type 
metal and the resulting plate is fastened to a wooden block. 



182 ELEMEXTS OF ELECTRICITY. 



CHAPTER 22. 
THE STORAGE BATTERY. 

236. Reversibility of Cells. — Should a simple zinc-carbon cell 
be connected in closed circuit, a current will be produced and 
while it is flowing the zinc will waste away and go into solution 
as zinc sulphate, the electrolyte will grow weaker and hydrogen 
will be evolved at the carbon plate. Suppose now the circuit to 
be broken and that there be inserted in it a battery or an electrical 
machine faced in the opposite direction to the original cell. If 
this battery or machine produces a greater electro-motive force 
than the cell, a current will be set up opposite to the original cur- 
rent and will flow through the cell in a reverse direction, that is, 
the simple cell now becomes an electrolytic cell (Par. 220). The 
zinc sulphate in solution will be decomposed, the zinc being rede- 
posited upon the zinc plate (Par. 224), the electrolyte increasing 
in strength and oxygen being released at the carbon plate, in other 
words, if the current continues to flow for a sufficient length of 
time the previous chemical action will be undone and, with the 
exception of the loss of a small amount of water in the form of 
hydrogen and oxygen, the cell will be restored to its primary con- 
dition. Such a cell is said to be reversible. It is evident that a 
primary cell in which the chemical action results in the escape in 
the form of gas of a portion of the active material can not be en- 
tirely reversible. 

237. Storage Battery. — A cell which is thus reversible and 
which when exhausted is regenerated by passing through it from 
an extraneous source of electrical energy a current opposite in 
direction to the flow of discharge, is called a secondary cell, or an 
accumulator, or, more commonly, a storage battery, although 
strictly the word "battery," as already pointed out, should be 
applied to a group of two or more cells. When such a battery 
approaches exhaustion it is said to be discharged, and the operation 
of restoring it is called charging. As commonly understood, a 
storage battery is one whose primary condition is that of exhaus- 



VOLTAIC ELECTRICITY. 183 

tion, that is, one which can not be used until it has first been 
charged. Reflection will show that the charging current must 
enter the battery by the same pole from which the discharging 
current leaves, that is, by the positive pole. The academic dis- 
tinction between the positive pole and the positive plate of voltaic 
cells (Par. 193) is not observed in dealing with storage batteries 
and the positive plate is that which carries the positive pole and is 
that plate from which the current issues on discharge and by which 
it enters on charge. In these storage batteries there is no elec- 
tricity stored up. The charging current enters at the positive 
pole, passes through the battery and leaves by the negative pole, 
but in its passage it performs chemical work or builds up a certain 
chemical potential which later produces electrical energy when the 
proper connections are made. 

238. Elements of a Secondary Cell. — Experiments have been 
conducted with many substances to determine their fitness for 
the elements of a secondary cell but, with the exception of 
the recently introduced nickel-iron-potassium hydroxide cell of 
Edison (Par. 250), the great majority of storage batteries employ 
positive plates of lead peroxide, Pb0 2 , negative plates of pure 
lead, and an electrolyte of dilute sulphuric acid of a specific 
gravity of about 1.20, or about one part of acid by bulk to five of 
water. There are many objections to lead; it is very heavy, it is 
soft, and the workmen in it frequently suffer from lead poisoning. 
There must then be some peculiar qualities of lead which outweigh 
these disadvantages. Upon examining its chemical properties we 
are at once struck by the fact that it is the only commercial metal 
whose sulphate is insoluble. When, therefore, the electrolyte 
attacks the plates and produces lead sulphate, this salt does not 
pass off into solution but remains at the precise spot where formed 
and when the cell is charged the sulphate is reconverted into lead 
without any change of position. Repeated charging and dis- 
charging, therefore, does not materially alter the shape of the 
plates. 

239. Preparation of the Plates. — The peroxide of lead of the 
positive plate and the pure lead of the negative plate are designated 
as the active material of the cell. Since the chemical action, the 
source of the electrical energy developed, takes place only at 
the surface of contact of the active material and the electrolyte, 



184 ELEMENTS OF ELECTRICITY. 

the object held in view in preparing the plates is to give to this 
active material the maximum amount of surface. This object is 
attained in any one or combination of three ways. 

(a) Mechanical. — The plate may be deeply incised, or grooved, 
or fluted, or thin tape-like ribbons of lead may be corrugated, 
coiled up and inserted in apertures in the plate proper, or the active 
material may be applied to the plate as a paste, or it may be 
powdered and placed in perforated receptacles which are attached 
to the plate. 

(b) Chemical. — The metal may be eaten by acids until it 
becomes more or less spongy, or it may be cast mixed with a 
granulated substance which is subsequently dissolved out leaving 
the plate porous. 

(c) Electrolytic. — The plate may have attached to it or enclosed 
in cavities in it a salt of the metal, which salt, as may be desired, 
is either converted by electrolytic action into the peroxide or else 
reduced to a finely divided metallic state. 

Since neither the peroxide nor the spongy lead possess the 
requisite mechanical strength for plates, the active material is 
generally contained or supported in spaces between the ribs of a 
grid-iron shaped frame of lead. On this account, the plates are 
frequently called grids. 

240. The Plante Cell. — The first storage batteries were pro- 
duced by Plante in 1860. The plates were prepared by placing 
face to face, and separated by a layer of felt two thin sheets of lead 
which were rolled up spirally into a cylinder and placed in a cell 
containing dilute sulphuric acid. On passing a current through 
the cell the water was decomposed (Par. 219) and the oxygen 
released at the anode converted the surface of this plate into the 
peroxide. After a number of hours the current was reversed. 
The other plate now became the anode and was converted into the 
peroxide, while the hydrogen released at the cathode reduced the 
former peroxide to metallic lead, leaving it in a spongy condition. 
The current was thus reversed several times and each time the 
chemical action penetrated more deeply into the plates, or the 
plates were said to be "worked up." It will be seen in the follow- 
ing paragraphs that the principle of the preparation of the plates 
in more modern storage batteries is the same, although the details 
are different. 



VOLTAIC ELECTRICITY. 



185 



241. The Chloride Accumulator. — A well known form of 
storage battery is the chloride accumulator, so called because in 
the manufacture of the earlier forms the chlorides of zinc and lead 
were used. In preparing the negative plates, the powdered 
chlorides of lead and zinc were intimately mixed and melted and 
the fused mass was then cast into little blocks a quarter of an inch 
thick and about an inch square. These blocks were then placed 
in a mould, arranged in regular order and evenly spaced, and 
melted lead was poured into the mould. The resulting plate can 
be compared to a window sash, the lead corresponding to the wood 




r c l 

[ c 

HE 



ooo 
aaa 
ooo 
ooo 
ooo 
ooo 
ooo 
ooo 



ooooo 
ooooa 
ooooo 
aaaaa 
ooooa 
ooooo 
ooooa 
ooooo 



c 



^^m 



Q 






mm 



Fig. 109. 



work and the chloride blocks to the panes (Fig. 109 a). The plate 
was next soaked in water which dissolved out and removed the 
zinc chloride and left the lead chloride in a porous condition. 
Finally, this plate was made the cathode of an electrolytic cell 
and a current passed through it until the lead chloride was entirely 
reduced to spongy lead. In more recent forms the negative grid 
is composed of two faces each containing shallow rectangular 
cavities, the bottoms of these being finely perforated. They are 
filled with one of the oxides of lead, the two faces are then pressed 



186 ELEMENTS OF ELECTRICITY. 

together and rivetted firmly. The perforations permit the 
electrolyte to reach the lead oxide which by electrolytic action is 
reduced to spongy lead. 

The grid for the positive plate was made of lead which, for the 
sake of hardness, was alloyed with a small amount of antimony. 
It was cast with rows of circular openings (Fig. 109 b) which were 
not cylindrical but contracted towards the center of the plate. 
Thin corrugated ribbons of lead were rolled up into cylinders and 
pressed into these openings, the shape of the openings causing the 
cylinders to be held firmly. The plate was then made the anode 
of an electrolytic cell for about 30 hours, the oxygen released by 
the current converting a part of the lead into lead peroxide. The 
amount of active material is sometimes increased by filling the 
crevices in the corrugated tape with a paste of either red lead, 
Pb 3 4 , or of litharge, PbO, both of which become peroxide in the 
electrolytic cell. 

242. Shape and Size of Plates. — The plates, except the largest 
sizes, are square. The thickness of the smaller plates is one- 
quarter of an inch but for the sake of strength this is increased to 
one-half inch in the larger ones. The size varies with the current 
which the battery is designed to furnish when discharged at its 
normal rate, that is, at the rate which experience has shown can 
not be exceeded without more or less injury to the plate. This is 
generally taken as about six amperes per square foot of positive 
plate surface. Thus the E plate of the chloride accumulator 
measures 7.75x7.75 inches, or 120 square inches, which is five- 
sixths of a square foot, and the normal rate is given by its manu- 
facturers as five amperes. If the cell contains three of these plates, 
its normal rate is 15 amperes, etc. The plates of this battery are 
designated by the letters of the alphabet, the B plate being the 
smallest and measuring 3x3 inches, and each has twice the active 
surface and twice the normal rate of the next smaller size. Thus 
the normal rate of an F plate is ten amperes. 

243. Grouping of Plates. — The plates are cast with three lugs 
at the top. Two of these rest on the opposite sides of the cell 
when the plate is in position, support its weight and keep it an 
inch or so above the bottom of the cell (Fig. 110). The third is 
used to join the similar plates of one cell to a common terminal or 
cross strap. They fit into holes mortised in the cross strap and 



VOLTAIC ELECTRICITY. 



187 



are "burned" to the strap by a hydrogen flame, the hydrogen 
reducing any oxide on the surface of the molten metal and thus 
allowing a perfect joint to be formed. 

The number of plates is always odd, there being one more 
negative plate, so that each positive plate has a negative plate 
presented to each of its faces. The smallest number of plates is 
therefore three; on the other hand, cells are made which contain 
75 or more. The total number of plates per cell is indicated by a 
subscript after the letter designating the size, as B z , C b , etc. 




The cells, except those of large size and those for use in vehicles, 
are of glass. They frequently rest in shallow boxes which contain 
sand so as to distribute the weight evenly over the bottom, the 
boxes in turn resting on insulating glass supports. The cells for 
vehicles are of hard rubber and have rubber covers. The larger 
cells are lead-lined wooden tanks. The largest chloride accumu- 
lator cell contains 75 plates, each 15x31 inches, weighs three tons 
and will furnish 1500 amperes for eight hours. 



188 



ELEMENTS OF ELECTRICITY. 



Should dissimilar plates touch each other directly or be put in 
contact through any sediment at the bottom of the cell, they will 
be short circuited (Par. 306). For this reason they are held apart 
by some form of fender or "separator," and, as stated above, are 
supported an inch or so above the bottom of the cell. Formerly 
rods of glass or of hard rubber were used as separators but now 
preference is given to thin wooden boards of the thickness used in 
making berry boxes. Owing to this compact arrangement of the 
plates the internal resistance of a storage cell is very small (Par. 
294), usually something less than one-thousandth of an ohm. 

244. Reaction on Discharge and Charge. — When the cell has 
been completely charged, the active material of the positive plate 
being lead peroxide and that of the negative plate spongy lead, 
we have the requisite conditions for a simple voltaic cell (Par. 201), 
that is, two conducting substances immersed in a liquid which 
attacks one more freely than it does the other. When the circuit 
is closed the electrolyte attacks the negative plate (Fig. Ill a) 





Fig. ill. 

producing lead sulphate. Hydrogen released at the positive plate 
is converted into water at the expense of the oxygen of the per- 
oxide, that is, the peroxide is the depolarizer of the cell. When the 
peroxide has thus been deoxidized, the remaining lead is attacked 
by the electrolyte, producing lead sulphate and action ceases. In 
practice however, the cell is recharged before this limit is reached. 
The reaction may be written 



Positive Electro- 
Plate lyte 


Negative 
Plate 


Positive Electro- 
Plate lyte 


Negative 
Plate 


Pb0 2 + 2H 2 S0 4 + 


Pb = 


= PbS0 4 + 2H 2 


+PbS0 4 



although actually it is more complicated. 



VOLTAIC ELECTRICITY. 189 

It will be noted that during discharge the acid is withdrawn 
from the electrolyte and goes into combination with the plates 
and that water is released in its stead, that is, the E. M. F. of the 
cell decreases, the resistance of the electrolyte increases and its 
specific gravity decreases. 

The reactions on charge are the reverse of those on discharge. 
Fig. Ill b represents diagrammatically an electric generator send- 
ing a current through the cell, both of whose plates are supposed 
to have become lead sulphate. The water of the electrolyte is 
decomposed, the hydrogen removing the S0 4 from the plates and 
forming again H 2 S0 4 , and the oxygen released at the positive plate 
reconverting the lead into the peroxide. The reaction is 



Positive 


Electro- 


Negative 


Positive 


Electro- 


Negative 


Plate 


lyte 


Plate 


Plate 


lyte 


Plate 



PbS0 4 + 2H 2 + PbS0 4 = Pb0 2 + 2H 2 S0 4 + Pb 
As a result of this, the E. M. F. of the cell rises, the resistance 
of the electrolyte decreases and its specific gravity increases. 

245. Charging. — The current for charging a storage battery is 
generally furnished by a generator, though a battery of a few cells 
may be charged from a larger battery. This current, as has al- 
ready been stated, is brought in at the positive pole of the battery. 
Its E. M. F. should be from 5 to 10 per cent greater than that of 
the battery and since the E. M. F. of the battery rises as the 
charging progresses, there must be some arrangement by which 
the charging E. M. F. may be increased correspondingly. If the 
E. M. F. of the source of supply be less than that of the battery, 
the latter during charging must be subdivided into groups which 
are conveniently charged in parallel (Par. 336). When a batters- 
is discharged it must be recharged at once, for if the discharged 
plates remain in the acid for even a short time they become in- 
jured (Par. 247). The rate at which the battery is charged is fixed 
by the makers and averages about ten per cent less than the normal 
rate of discharge. It can not be exceeded without risk. At least 
as much time is required to charge a battery as to discharge it. 
When a battery is put into commission for the first time it has to 
be charged at the normal rate for from 45 to 55 hours continuously 
but thereafter the normal time is about eight or nine hours. 

246. Indications of Charge. — It is important to be able to tell 
when a battery is properly charged. The indications usually 
relied upon are the following: — 



190 



ELEMENTS OF ELECTRICITY. 



(a) Voltage. — A new cell, when fully charged and while still 
receiving the charging current, should have a voltage of 2.5 or even 
slightly more, but this decreases with age. When current is 
drawn from the cell the voltage almost immediately falls to 2.05 
or 2.0 after which it decreases slowly and steadily until the cell 
approaches exhaustion at which point it begins to drop rapidly 
(Fig. 112). A cell should never be discharged to a lower voltage 
than 1.7 and if it reaches this point should be recharged at once. 
In actual charging the process is continued until three successive 
readings of the voltmeter at intervals of fifteen minutes show no 
further rise. Usually some average interior cell of the battery is 

VOLTS 

30 

7.S 

JJ.6 

ZA 

ZZ- 

2.0 

i.2 














































































































^" 










/-IIA n r- 






_*»'■ 
















. 


--"^ 




c 
























DlS 


:har^e 


===== - 




— ■ — « - 


























































i 


z 


3 


4 


-H0UR5- 




7 


S 


5 


6 



Fig. 112. 

selected as a ' 'pilot cell" and its voltage is taken as an indication 
of that of the others. In order that these observations may be 
of any value, the voltage must be taken while the battery is either 
being charged or discharged at the normal rate. 

(b) Specific gravity of the electrolyte. — Examination of the 
reactions given in Par. 244 shows that during charge sulphuric 
acid is driven out from its combination with the plates and is 
released in the electrolyte. The specific gravity of sulphuric acid 
(1.834) being nearly twice as great as that of water, that of 
the electrolyte rises accordingly. When discharged, the specific 
gravity of the electrolyte may fall as low as 1.175 or even less, 
and when charged it should lie between 1.200 and 1.210. The 
specific gravity is read from a hydrometer, a little lead- weigh ted, 
flattened glass float having a slender graduated stem and look- 



X 



VOLTAIC ELECTRICITY. 191 

ing somewhat like a thermometer (Fig. 113). As the density 
of the electrolyte decreases the hydrometer sinks deeper into 
the liquid; as it increases, the hydrometer floats higher 
and in each case the corresponding specific gravity is 
indicated by the graduation on the stem of the instrument 
reached by the surface of the electrolyte. 

(c) Gassing. — When bubbles of gas begin to rise freely 
in the cell, giving the liquid the appearance of boiling, the 
current has completed its work upon the plates and is 
decomposing the electrolyte, the charging therefore should 
not be pushed farther. These mixed gases are explosive, 
therefore the storage battery room should be well venti- 
lated and no flame should be taken into the room when 
the cells are gassing. / 

(d) Color of the plates. — When fully charged the positive 
plates are of a rich chocolate color, the negative plates a 
lead grey, and these colors afford the expert a means of 
judging of the state of charge. 

247. Troubles of Lead Batteries. — If a lead-sulphuric 
acid battery be charged or discharged at an excessive 
rate, or be allowed to stand discharged, the acid attacks fJ^L3 
the plates and forms a white coating supposed to be the 

basic lead-sulphate Pb 2 S0 5 . The plates are then said to be 
sulphated. This coating is insoluble and a non-conductor and 
practically removes from action the part of the plate which it 
effects. When not too extensive, it may sometimes be removed 
by repeated charging and discharging of the cells. 

The crystals of sulphate forming within the porous portions of 
the plate sometimes act as wedges and cause the plate to buckle, 
that is, to bulge out in a dish shape. This usually loosens and 
causes a loss of the active material of the plate and may produce 
a short circuit with the adjacent plates of the cell. 

248. Care of Lead Batteries. — Lead batteries must be given 
constant attention. Charging should be done at regular intervals 
and the battery must never be allowed to stand discharged. Each 
cell should be numbered; these numbers should be entered in a 
blank book and a weekly record should be kept of the voltage and 
the specific gravity of each cell. Inspection of this record will 
frequently reveal incipient trouble in individual cells and will thus 




192 ELEMENTS OF ELECTRICITY. 

enable corrections to be applied before serious damage has occurred. 
A battery should not long remain idle. If it is not to be used 
for some months it should be put out of commission. It is charged 
fully, thus expelling into the electrolyte the acid in combination 
with the plates. The electrolyte is then syphoned off into carboys, 
the cells filled with water and allowed to stand for 48 hours, after 
which the water is drawn off. 

249. Objections to Lead Batteries. — The principal objections 
advanced against lead batteries are — 

(a) Poisonous effect of lead upon the workmen engaged in the 
manufacture of the plates. 

(b) Excessive weight of the plates, lead being the heaviest of 
the commercial metals. 

(c) Fragility of the cells and inability to stand shocks and jars. 

(d) Need of constant supervision by an expert electrician for 
proper care of the battery. 

(e) Injury resulting to the battery if it remains uncharged for 
any length of time. 

(f) Injury resulting to the battery if it remains long charged 
and hence necessity of charging and discharging even when use 
of battery is not required. 

(g) Injury produced by short circuits or by charging or dis- 
charging at excessive rates. 

(h) Injury produced by using the battery if the temperature 
rises above 100° F. 

(i) Loss of active material from the plates. 

(j) Production of acid vapors highly irritating to the throat 
and lungs and corrosive to surrounding objects of metal. 

(k) Production of explosive gases. 

(1) Loss of charge on standing. This amounts to about 25 per 
cent per week. 

The foregoing indicates that the lead battery is most advan- 
tageously employed when it is installed in a suitable build-- 
ing and subjected to constant use under the supervision of a 
trained electrician, and that it is not well adapted for service in 
vehicles used roughly and irregularly and cared for by unskilled 
attendants. 



VOLTAIC ELECTRICITY 



193 



250. The Edison Storage Battery. — The Edison storage battery 
is designed primarily for use in vehicles and has been developed 
to avoid as far as possible the objections enumerated in the pre- 
ceding paragraph. In this battery the active material of the 
positive plate is nickel peroxide, Ni 2 3 , that of the negative plate 
is finely divided iron, and the electrolyte is a 21 per cent solution 
of potassium hydroxide, KOH, to which is added a small amount 
of lithium hydroxide. The grids are of nickel-plated steel. 

The active material of the positive plate, initially in the form of 
nickel hydroxide, Ni(OH) 2 , is packed in small pencil-like perforated 
tubes of nickel-plated steel which are securely fastened to the grid 
(Fig. 114 a). To improve the conductivity of this active material, 



ixedidk 





Fig. 114. 

it is interspersed with layers of extremely thin nickel flakes, there 
being as many as 350 layers in each tube in a length of about four 
inches. These tubes are banded at intervals by steel hoops which 
prevent any expansion due to swelling of the material within. The 
active material of the negative plate, primarily ferrous oxide, 
FeO, is packed into flat perforated pockets of nickeled steel which 
are forced into the grid under pressure. A small per cent of mer- 
cury is added to the oxide to improve its conductivity. 



194 ELEMENTS OF ELECTRICITY. 

The plates are held together by nickeled-steel cross bolts which 
also carry the terminals. Opposite plates are held apart by rubber 
separators. The cells are of nickel-plated sheet steel, corrugated 
for rigidity (Fig. 114 b). The assembled plates, protected on all 
sides by rubber fenders, are fitted tightly into the cell which is 
then closed by a steel lid which is welded on. This lid contains 
an opening through which electrolyte may be introduced and is 
arranged with a valve which permits gas to escape from the cell 
but prevents gas from entering. Potassium hydroxide has a great 
affinity for carbonic acid gas, C0 2 , which, if the cell were left open, 
would rapidly injure the electrolyte. 

There are two regular sizes of plates designated A and B. The 
A plates are the larger, the rectangular portion being about 
5x12 inches. A number following the letter, as A-4, indicates 
not the total number of plates but the number of positive plates 
in the cell. The normal rate of discharge of an A plate is seven 
and a half amperes. The normal rate of an A-4 cell is therefore 
thirty amperes. 

251. Reactions of the Edison Battery. — In Par. 223 it was 
shown that when a current is passed through a solution of KOH 
the effect is merely to electrolyze the water. On the first charge 
the oxygen released at the anode converts the nickel hydroxide 
into the peroxide, thus — 

2Ni(OH) 2 +0 =Ni 2 3 +2H 2 

and the hydrogen 
released at the cathode reduces the iron oxide to metallic iron 
FeO + H 2 = Fe+H 2 

On discharge the reaction is as follows: 

Positive Electro- Negative Positive Electro- Negative 

Plate lyte Plate Plate lyte Plate 

Ni '°° + S S?f + Fe = 2NiO + \ *° H + FeO 
On charge this is reversed, or 

Positive Electro- Negative Positive Electro- Negative 

Plate lyte Plate Plate lyte Plate 

2NiO+ S* 0H + Fe0 = Ni 2 0„ + \ *° H + Fe 

From the preceding it is seen that the reactions in the cell con- 
sist in the transfer of oxygen back and forth and that the electro- 
lyte is unaltered. It may therefore be reduced to a minimum with 



VOLTAIC ELECTRICITY. 



195 



a corresponding saving of bulk and weight. It would also seem 
that it should last indefinitely but, as stated in the preceding 
paragraph, it absorbs and combines readily with carbon dioxide 
and on this account should be renewed yearly. 

252. Charging the Edison Battery. — Since the electrolyte 
remains unaltered during charge and discharge and since the 
plates are enclosed in an hermetically sealed steel case, the only 
indication of charge of an Edison cell is its voltage taken while 
charging or discharging. During charge the voltage gradually 
rises (Fig. 115) until when fully charged and receiving current it 

VOLTS 
1.0 

1.8 

1.6 

14 

i.a 
J.o 





















_ . _ _ 








— — — — 






CHARGE, 


_, 





— 




„*■" 














<v 














"-- __ 






































^■•v^ 




1 


2 


5= 

3 


Hr HOURS — 

4 


>$* 


6 


7 



Fig. 115. 

reaches a maximum of 1.84. When current is drawn from the cell 
the voltage drops at once to about 1.4 and then falls gradually, 
averaging about 1.2 volts until near the end when it drops rapidly 
to one volt. On the average, a battery is charged at the normal 
rate in seven hours and discharges in about six. 

253. Advantages and Disadvantages of the Edison Battery. — 

The advantages of the Edison battery are in marked contrast to 
the disadvantages of the lead battery as enumerated in Par. 249. 
Thus— 

(a) Although the salts of nickel are poisonous, the workmen 
preparing the plates are free from danger. 

(b) The plates are lighter than corresponding lead plates. 

(c) The cells could hardly be improved as regards strength. 
They are uninjured by the most violent jolts and jars to which a 
vehicle may be exposed. 

(d) They require a minimum of attention. 

(e) They may be left without injury at any state of charge or 
discharge. 



196 ELEMENTS OF ELECTRICITY. 

(f) They may be charged or discharged at excessive rates, may 
be overcharged, short circuited, or even reversed without per- 
manent injury. 

(g) They produce no irritating or corrosive fumes, in fact, by 
the absorption of carbon dioxide they purify the air. This last 
renders them especially valuable in submarines. 

The disadvantages of the Edison cell are — 

(a) Low voltage; only 1.2 as compared to nearly 2.0 of the lead 
cell, hence a greater number of cells required. 

(b) Decrease of activity at temperatures below 40° F. 

(c) Greater cost than lead cell. 

The efficiency (ratio of energy delivered by the cell to that 
spent in charging it) of the lead cell is about 75 per cent; that of 
the Edison cell is only 60 per cent, but weight for weight the 
efficiency of the Edison cell is the greater. 

254. Use of Storage Batteries. — It requires more time to charge 
a storage battery than it does to discharge it. We have just seen 
that the efficiency does not exceed 75 per cent. There is therefore 
a loss of both time and energy and the question arises why should 
storage batteries be employed. This is best answered by an 
enumeration of some of the commoner uses of storage batteries. 
These are — 

(a) As a portable source of power and light for vehicles, launches 
and submarine boats; also for furnishing the ignition spark for 
automobiles. 

(b) As a source of power and light in public buildings, hotels, 
etc., to run lights, elevators, etc., after the engines have been shut 
down for the night and thus to save the expense of an extra shift 
of engineers and firemen. 

(c) As a reserve in electrical power plants, supplying power 
during a temporary stopping of the engines for adjustment, over- 
hauling or repairs. 

(d) To light the magazines of a fortification and to operate the 
mine and the range finding systems. 

(e) To carry the "peak loads" of an electric railroad or of a 
lighting plant. Such a plant must be able to supply the maximum 
current required during the rush hours. It is also operated most 
efficiently when the engines are run at a uniform rate. If it sup- 
plied constantly the maximum current there would be much 



VOLTAIC ELECTRICITY. 



197 



waste during the slack hours. The curve in Fig. 116 may be taken 
to represent the operation of a trolley line during 24 hours, the 
horizontal axis being the axis of time, the vertical heights repre- 
senting the power supplied by the electric plant and consequently 



A 




B 


IIP 


v/7 • j n 

y III 

f i « 'I 
i i i i 


i 

i 



iZ?M. 



4 A.M. 



8 A.M. 



ifcM 

Fig. 116 



4P.M 



P.M 



JJtP.M 



the area of the curve representing work performed. If the line 
AB represents the constant output of the engines, the shaded 
areas represent surplus energy which may be applied to charging 
a storage battery, the battery in turn being called upon to give 
back energy when the peak loads occur at 8 A. M. and at 6 P. M. 
There are other uses of the storage battery but they can not 
be explained until our subject has been further developed. 



198 ELEMENTS OF ELECTRICITY. 



CHAPTER 23. 

THEORY OF ELECTROLYTIC DISSOCIATION. 

255. Interdependence of the Physical Sciences. — The more 
our knowledge of the physical sciences is increased, the more we 
realize their interrelation and their interdependence. The study 
of no particular one can be successfully pursued if we exclude the 
help afforded and the side lights thrown upon it by others. This 
is notably so in the case of electricity. For a proper understanding 
of the present accepted theory accounting for the phenomena of 
voltaic electricity, we must turn to physical chemistry and to 
develop our explanation must begin with certain facts which at 
first sight appear to have not even a remote connection with our 
announced subject. 

The following outline will assist the student in following the 
thread of connection between the facts which will now be brought 
out: 

1. Avogadro's law and a derived corollary applicable to gase- 
ous pressure are explained (Par. 256) . 

2. Exceptions to the law of gaseous pressure are shown to be 
due to dissociation which is defined (Pars. 257-258). 

3. Osmotic pressure is described and its observation and meas- 
urement explained (Pars. 259-262) . 

4. Osmotic pressure is shown to follow the laws of gaseous 
pressure (Pars. 263-266). 

5. Abnormal osmotic pressures are, like excessive gaseous 
pressures, shown to be capable of explanation under the supposi- 
tion of dissociation, otherwise called ionization (Pars. 267-268). 

6. Ionization is further explained (Pars. 269-274) . 

7. Electrolytic properties are shown to depend upon ionization 
(Pars. 275-279). 

8. Electricity is shown to be atomic in character (Par. 280). 

256. Laws of Variation of Gaseous Pressure. — Avogadro's 
Law, of fundamental importance in Chemistry, is to the effect 
that under like conditions of temperature and pressure, equal 



VOLTAIC ELECTRICITY. 199 

volumes of all gases, simple or compound, contain the same num- 
ber of molecules. If we should have a series of cylinders of exactly 
the same capacity and should fill one with oxygen, one with hydro- 
gen, one with carbon dioxide, one with marsh gas, and so on, each 
being at the same temperature and exposed to the same pressure, 
then each would contain exactly the same number of molecules. 

Suppose one of these cylinders of the same diameter as the 
others should be twice as tall. If this one be filled with gas it will, 
from the above, contain twice as many molecules as the others. 
Place a piston in the mouth of this cylinder and press it down until 
the volume of the enclosed gas be reduced one-half, that is, until 
it becomes the same as that of the other cylinders. The space 
beneath the piston now contains twice as many molecules as the 
other cylinders contain. From Mariotte's Law, temperature 
remaining constant, the volume of a gas varies inversely as the 
pressure. The pressure upon the compressed cylinder is therefore 
twice that upon the others. Hence we may state, as a corollary 
to Avogadro's law, that for a constant temperature and volume, the 
pressure of a gas varies directly as the number of molecules enclosed. 

From a combination of Charles' and Mariotte's Laws it is shown 
that for constant volume, the pressure produced by an enclosed 
gas varies as the absolute temperature. (The absolute tempera- 
ture is obtained by adding the constant 273 to the temperature 
as indicated on the Centigrade scale.) We therefore see that the 
pressure of a gas confined in a given volume varies (a) with the 
number of molecules enclosed and, (b) with the absolute tempera- 
ture. 

257. Decomposition and Dissociation. — In general, compound 
substances if heated to a sufficiently high temperature are resolved 
into simpler ones. If when these simpler substances are cooled 
to the primary temperature they remain separate, the original 
compound body is said to have undergone decomposition. On the 
other hand, if when the temperature falls the simpler substances 
recombine and reproduce the original substance, this body is said 
to have undergone dissociation. Decomposition is therefore 
permanent while dissociation is transient and continues only so 
long as the agency which brought it about is operative. 

258. Example of Dissociation by Heat. — Ammonium chloride, 
NH 4 C1, like other ammonium salts, is volatilized with compar- 



200 ELEMENTS OF ELECTRICITY. 

ative ease. Its molecular weight being 53.5, the gas produced by 
the volatilization of 53.5 grams should exert the same pressure 
as that produced by a molugram of any other gas confined in an 
equal volume and at the same temperature. (A molugram is the 
molecular weight expressed in grams, as for example 2 grams of 
hydrogen, 28 grams of nitrogen, 44 grams of carbon dioxide, and 
so on.) By actual experiment however the pressure is found to be 
twice as great. From (a) Par. 256 therefore, there must be twice 
as many molecules present in the gaseous NH 4 C1 as there are in 
the other gases. The explanation is that the NH 4 C1 has been 
dissociated by the heat, each molecule becoming two, one of 
ammonia, NH 3 , the other of hydrochloric acid, HC1. That this 
is so may be proven in several ways. First, if NH 4 C1 became a 
gas without dissociation, the specific gravity of this gas referred 
to hydrogen should be 26.7 while it is actually only 13.35 which 
is the specific gravity of a mixture of equal volumes of NH 3 and 
HC1. Second, the specific gravity of EC1 being 18.2 while that 
of NH 3 is only 8.5, if the dissociation takes place in a vertical 
closed tube, the heavier HC1 will settle at the bottom, the lighter 
NH 3 rising to the top. If by means of a stop cock at the middle 
of the tube the two halves be now cut apart and after cooling be 
tested separately, the contents of the upper half will be found to 
be alkaline, that of the lower half acid. 

259. Osmosis and Osmotic Pressure. — Suppose the space 
below the piston of a vertical cylinder to be filled with a gas under 
normal pressure. If the piston be raised, thereby increasing the 
space beneath it, the gas will be found to have spread through this 
new space completely filling it. There is therefore a force or 
pressure which compels a volume of gas to diffuse or to swell 
out and occupy a greater space when it has the opportunity to 
do so. 

Again, if in the bottom of a vessel there be placed a concen- 
trated solution of a salt and if then there be poured carefully on 
top of this solution a layer of pure water, in a short while the dis- 
solved salt, in defiance of gravity, will have spread upward and 
throughout the liquid until the latter is all of a uniform density. 
By using a colored salt the progress of the diffusion can be easily 
observed. There is therefore a force, similar to the gaseous pres- 
sure described above, which urges the particles of a dissolved 
substance to spread equally throughout the solvent. 



VOLTAIC ELECTRICITY. 



201 



There are known various membranes, some animal, some 
vegetable, and some artificial, which will permit the passage 
through them of certain liquids but will prevent the passage of 
other substances dissolved in these liquids. On account of this 
property these membranes are called semi-permeable. If a bladder 
(which is one of these) be filled with an aqueous solution of a salt, 
tied tightly, and then submerged in a vessel of pure water, it will 
gradually distend and may finally burst. This is explained by 
saying that the substance in solution is urged by the pressure 
described above to spread out into the surrounding solvent but 
being unable to pass through the membrane it pushes against it 
and distends it, thus allowing the water on the outside to enter. 
Although this explanation is admittedly a poor one, the phenom- 
enon does occur and is called osmosis, and the force exerted 
upon the membrane by the dissolved molecules is called osmotic 
pressure. 

In the above illustration we have assumed an aqueous solu- 
tion of a salt but under proper conditions osmosis takes place 
whatever the nature of the solvent or of the dissolved sub- 
stance. 

260. Demonstration of Osmotic Pressure. — Osmotic pressure 
may be conveniently shown as follows. A membrane is stretched 
and tied over the mouth of a glass funnel which is then inverted 
and filled to the neck with a solution, say 
of copper sulphate. The inverted funnel 
is then inserted, as shown in Fig. 117, in a 
vessel of pure water until the surface of 
the water and that of the liquid in the 
neck of the funnel are at the same level. 
The copper sulphate solution will be ob- 
served to rise slowly in the neck of the 
funnel and may continue to do so for 
several weeks, attaining its maximum 
height when the hydrostatic pressure of 
the liquid in the tube just prevents the 
passage of additional water through the 
membrane and the further dilution of the Fig - 11T - 

contained solution. The osmotic pressure and the hydrostatic 
pressure are now in balance and by measuring the latter we 
determine the former. 




202 ELEMENTS OF ELECTRICITY. 

261. Measurement of Osmotic Pressure. — The arrangement 
described in the preceding paragraph is not well suited for the 
measurement of osmotic pressures. These are relatively great. 
The osmotic pressure produced by a dilute solution of sugar has 
driven a column of water to a height of nearly 70 feet, and this 
pressure is frequently exceeded. The membrane would not stand 
these pressures and it is impracticable to use tubes of such length. 
Again, the membrane is not absolutely impermeable to the salt 
and some escapes into the surrounding solvent. Also, the mem- 
brane is distended, thereby increasing the volume of the confined 
solution and materially altering the degree of concentration. For 
these reasons accurate determinations of osmotic pressure were 
not made until within recent years when it was discovered that 
certain colloidal or gelatinous precipitates, notably the ferro- 
cyanide of copper, act, so far as permeability is concerned, as 
ideal membranes. The strength of a film of such a precipitate is 
however very small and in order that it may withstand the pres- 
sure to which it is to be subjected it must be supported in some 
way. This object is now attained by depositing the film within the 
substance of a finely porous unglazed porcelain cup. These cups, 
about two inches tall and three-quarters of an inch in diameter, 
are first filled with a solution of potassium ferrocyanide which 
slowly soaks into the walls. They are then immersed in a solution 
of copper sulphate, which soaks in from the outside, and when the 
two liquids encounter each other the precipitate is formed. The 
actual process requires several days' time and involves a number 
of precautions not necessary to mention here. Into the mouth of 
the prepared cup are cemented the tube up which the liquid is to 
rise and a second tube with a stop cock by which the solution is 
introduced. The vertical or pressure tube is sealed at the top and 
the osmotic pressure may be determined by the amount of com- 
pression of the air above the liquid. In practice, the pressure tube 
is a mercurial manometer. By using these closed tubes to measure 
the pressure, the amount of the solvent which enters the cup is 
reduced to a minimum and the concentration of the solution is 
altered but little. 

262. Observations of Pfeffer. — The botanist, Pfeffer, in his 
investigations in plant physiology, made, with the apparatus just 
described, a series of observations upon the osmotic pressure pro- 
duced under various conditions by dilute solutions of organic 



VOLTAIC ELECTRICITY. 203 

compounds such as sugars, alcohols, etc. His results were pub- 
lished in 1877 but at that time attracted no special attention and 
it remained for Arrhenius and Van't Hoff to discover some ten 
years later the value of his data and its bearing upon the theory 
which we shall shortly explain. 

263. Osmotic Pressure Varies Directly with Number of Mole- 
cules Dissolved in Given Volume of Solution. — Pfeffer found 
that for these dilute solutions the osmotic pressure increased 
directly with the strength of the solution, that is, if the concen- 
tration (and hence the number of molecules in solution) be 
doubled, the osmotic pressure is likewise doubled, etc. His 
results for cane sugar were as follows: 

Strength of Osmotic -Ro+^ ^ 

Solution Pressure Katl ° S 

1% 510 mm. 510 

2% 1016 mm. 508 

4% 2082 mm. 520 

6% 3075 mm. 512 

In this table, while the pressures do not bear to each other the 
exact theoretical ratio, the variations therefrom are not greater 
than are to be expected from experimental errors and from the 
fact that the observations were not taken under precisely the same 
conditions of temperature, although they were made within a 
range of less than three degrees Centigrade. 

Comparing different substances, he found that while the osmotic 
pressure of a one per cent solution of cane sugar at 15.5° C was 
520.5 mm., that of a one per cent solution of raffinose at the same 
temperature was only 299 mm. The relation between these two 
numbers was not discovered until subsequent investigators 
worked upon his data. The formula for cane sugar is C12H22O11 
and its molecular weight is 342; that for raffinose is CisH 3 20i65H 2 
and its molecular weight is 594. Therefore, equal weights of the 
two do not contain the same number of molecules, a one per cent 
solution of raffinose containing fewer than a one per cent solution 
of sugar. Let us see how the pressures compare if we take the 
same number of molecules of each. Each litre of his cane sugar 
solution contained ^\% of a molugram. The same fraction of a 
molugram of raffinose would be ;J yv of 594 or 17.37 grams. If 
10 grams produced a pressure of 299 mm., what pressure would 
17.37 produce? 10 : 299 : : 17.37 : x 



204 ELEMENTS OF ELECTRICITY. 

whence x = 519.4 mm. as compared to the 520.5 mm. of the sugar 
solution. 

This and other examples show that substances in solution con- 
form to Avogadro's Law and to its corollaries, that is, equal 
volumes of solutions which at the same temperature exhibit the 
same osmotic pressure contain the same number of dissolved 
molecules, and also, other conditions being constant, the osmotic 
pressure varies directly with the number of molecules in solution. 

264. Osmotic Pressure Follows Mariotte's Law. — An exami- 
nation of Pfeffer's data will reveal the fact that osmotic pressure 
also follows the corollary to Mariotte's Law for gaseous pressure, 
that is, other conditions being constant the osmotic pressure 
varies directly with the absolute temperature. For example, the 
osmotic pressure of a one per cent solution of sugar at 14.15° C is 
510 mm. and at 32° C is 544 mm. Applying the law to the lower 

pressure 

510 : x-273+14.15 : 273+32 

whence x = 541.7 mm., 
agreeing closely with the observed pressure 544 mm. 

265. Osmotic Pressure of a Molecule in Solution Equals 
Pressure of a Gaseous Molecule under Equal Volume and Tem- 
perature. — We have seen from Par. 263 above that gW of a molu- 
gram of sugar or of other organic substance dissolved in a litre of 
water exerts at 15.5° C an osmotic pressure of about 520 mm. Let 
us see what pressure the same fraction of a molugram (and hence 
the same number of molecules) of hydrogen confined in the same 
space and at the same temperature would exert. One gram of 
hydrogen at 0° C and 760 mm. measures 11.165 litres, therefore, a 
molugram of hydrogen (2 grams), would under these conditions 
occupy 22.33 litres, and gW of a molugram would occupy .6529 
litre. At a temperature of 15.5° C this would dilate to .6914 
litre and if this be allowed to expand into the space of 1.006 litres 
(the space occupied by one litre of water to which 10 grams of 
sugar is added), the pressure would drop according to the propor- 
tion 

760 : x = 1.006 : .6914 

whence x = 522 .4 mm. 
We see then that the osmotic pressure of the sugar in solution 
is the same as the pressure exerted by an equal number of mole- 



VOLTAIC ELECTRICITY. 205 

cules of gas confined in the same space and at the same tem- 
perature. 

266. Van't HoflPs Generalization. — A consideration of the fore- 
going facts led to the generalization by Van't Hoff which is to the 
effect that "the osmotic pressure of a substance in solution is the 
same as the gas pressure which would be observed if the dissolved 
substance alone, in gaseous state and at the same temperature, 
occupied the volume of the solution." In other words, these sub- 
stances in solution behave, comparing osmotic pressure to gaseous 
pressure, precisely as if they had been converted into a gas and 
filled alone the space occupied by the solution. 

Independent theoretical considerations based upon the lowering 
of the freezing point and the raising of the boiling point by sub- 
stances in solution lead to the same conclusions and entirely 
corroborate Van't Hoff. 

267. Exceptions to Van't HoflPs Generalization. — Van't Hoff' s 
generalization applies, as we have seen, to dilute solutions of 
organic compounds. If the solutions become concentrated, the 
laws of osmotic pressure no longer hold strictly. This is thought 
to be parallel to the failure of gases, as they approach their point 
of condensation, to follow the laws of Charles and Boyle. 

If, now, we turn our attention to solutions of the inorganic 
compounds we find that the majority of them are exceptions and 
give osmotic pressures in excess of those required by theory. 
These exceptions embrace solutions of all the acids, all the bases 
and all the salts. It might seem therefore that in announcing as 
general a law to which the exceptions outnumber the agreements, 
Van't Hoff had overstepped the bounds of prudence. 

268. Dissociation Theory of Arrhenius. — In Par. 263 above 
we saw that osmotic pressure varied directly with the number of 
molecules in solution. Since in the exceptional cases the pressure 
is always greater than what it should be in theory, there must be 
a greater number of molecules present in solution than is indicated 
by the weights taken. To account for this greater number, 
Arrhenius advanced the theory that just as the excessive pressure 
produced by iodine, ammonium chloride, etc., when converted 
into vapor is explained by the fact that these substances are dis- 
sociated by the heat employed, so the excessive osmotic pressures 
are to be explained by the fact that the substances in solution 



206 ELEMENTS OF ELECTRICITY. 

undergo dissociation, or ionization, that is, split up into a greater 
number of parts. It is also a part of his theory that these part 
molecules or ions, whether they be atoms or compound radicles, 
exert the same osmotic pressure as an undissociated molecule. 
Some of the consequences following from this theory were so 
startling and so contrary to the views generally held by chemists 
that it was at first vigorously combated and reluctantly accepted 
as one by one the objections advanced against it were explained 
away. A full exposition of these consequences and replies to the 
objections would require an extended treatise. We can here do 
but little more than allude to a few of those most obviously con- 
nected with our subject. 

269. Why Ionization Takes Place in Solution. — Salts, acids 
and bases consist of two parts, a metal or hydrogen (or a radicle 
playing a similar part) combined with an acid radicle or, in the 
case of the base, with hydroxyl. The metal or hydrogen portion 
carries a positive charge of electricity; the remaining radicle 
carries an equal negative charge. These two parts may therefore 
be regarded as held together by the attraction of these opposite 
charges. The charges being relatively great (Par. 278) and the 
distance separating the parts being extremely small, the attraction ( 
is very great (Par. 53). In Par. 90 we saw that if two charged 
bodies which in air attract or repel each other with a certain force 
were placed in some other medium whose dielectric coefficient is 
K, then the force exerted between the two bodies would be only 
^th of what it was in air. The dielectric coefficient of water is 
given in Par. 92 as 80, or with the exceptions of hydrogen peroxide 
and hydrocyanic acid, greater than that yet determined for any 
other substance. The force which held the ions together is there- 
fore reduced to ^th of itself when the substance is brought into 
solution, and the ions drift apart. This view is corroborated by 
the variation in dissociation produced by using solvents of dif- 
ferent dielectric coefficients. 

270. How Ionization Takes Place. — Ionization takes place 
differently from the dissociation by heat. The metallic salts 
split into the metal and the acid radicle; the acids split into hydro- 
gen and the acid radicle; the bases split into the metal and the 
hydroxyl radicle. Now such radicles as NH 4 , OH, S0 4 , etc., which 
this requires, are unknown as separate entities. The ionization of 



VOLTAIC ELECTRICITY. 207 

KC1 supposes the presence in the water of atoms of potassium 
and of chlorine. If this be so, some of the chlorine should reveal 
itself by its color and odor. Further, it is well known that potas- 
sium placed upon water decomposes it with such violence as to 
produce flame and forms potassium hydroxide. None of these 
effects are produced and this was once regarded as a grave objec- 
tion to the theory. This objection is answered by the statement 
that ions, which may be denned as part molecules accompanied 
by electrical charges, i. e., with a deficit or an excess of one or 
more electrons, are different substances from the corresponding 
atoms or radicles, have different properties from these, and 
regain the properties of these only when they lose the charges. 
A metallic ion can go into solution only when it has a positive 
charge, and once in solution it can not be withdrawn until this 
charge is removed or neutralized. This ^an be shown experi- 
mentally thus. A plate of zinc dipped into hydrochloric acid is 
attacked vigorously and goes into solution. If, however, this plate 
be charged negatively, the action of the acid immediately ceases. 
So long as the potassium ion carries a positive charge it remains 
in solution, but when this charge is withdrawm by contact with the 
negatively-charged cathode the potassium regains its usual proper- 
ties and decomposes the water. 

271. Ionization Incomplete.— Should NaCl in solution be com- 
pletely ionized, the osmotic pressure produced would be twice 
that produced by an equal number of molecules of sugar. Barium 
chloride, BaCl 2 , since it ionizes into Ba, CI, CI, should produce 
three times this pressure. Were this the case, doubts about 
Arrhenius' theory would disappear, but it is not the case. The 
osmotic pressure of NaCl is not twice that of a sugar solution of 
the same molecular concentration. The explanation is that these 
salts do not completely ionize. At ordinary temperatures moder- 
ately dilute solutions of salts, strong acids and strong bases ionize 
from 80 to 90 per cent. However, as the dilution increases so does 
the dissociation and it approaches the theoretical figure when the 
dilution reaches one molugram per 1000 litres. 

272. Experimental Demonstration of Free Ions. — The presence 
of free ions was shown by Ostwald in the following experiment. 
A horizontal glass tube (Fig. 118) about one-half inch in diameter 



208 



ELEMENTS OF ELECTRICITY 



and some 20 inches long is bent up at right angles at the ends, 
these terminal portions being expanded to the size of a test tube 
and a piece of platinum wire C being fused through the bottom of 
the end B. The tube is filled with dilute sulphuric acid. In the 
end A is inserted a rubber stopper through which passes an 




Fig. 118. 



amalgamated rod of pure zinc. In the end B is inserted a stopper 
carrying a slender glass manometer M which is filled with water, 
colored for ease of observation. The zinc rod is connected to the 
positive pole of a battery of five or six cells, D; the platinum wire 
C is connected through the key K to the negative pole. The 
instant the key is closed, the manometer indicates an increase of 
pressure in B due to the hydrogen released at C. 

Just before the key was closed this hydrogen must have existed 
in the immediate vicinity of C in the form of free ions. From Par. 
270 they must have carried positive charges. But the cathode C 
was also positively charged and these ions were therefore repelled. 
As soon, however, as the key was closed, the charge on C was 
withdrawn, the hydrogen ions moved up to C, gave up then- 
charges and then recovered their status as free hydrogen atoms. 

273. Ions Not from Same Molecule. — According to the older 
theories, when the circuit was closed the zinc and sulphuric acid 
in A reacted, producing zinc sulphate and hydrogen and this 
hydrogen travelled from A to B and appeared at C. 

The following considerations will show that it is impossible that 



VOLTAIC ELECTRICITY. 209 

the hydrogen atoms released in A should be instantly shot across 
the 15 or 20 inches of electrolyte to C. By moderate exertion a 
small lead ball may be thrown several hundred feet. If this ball 
be cut up into fine shot the force required to throw it to this dis- 
tance would be very much greater. If it be reduced to dust we 
could not command sufficient force, and a particle of dust might 
contain several million atoms. Finally, the hydrogen atom is over 
200 times lighter than the lead atom and instead of moving 
through air moves through the liquid. It is thus seen that the 
force required would be beyond all reason. 

As a matter of fact, the ions move from both electrodes in 
opposite directions and at different rates of speed. These rates 
have been accurately measured. The swiftest of the ions, the 
hydrogen, moves under ordinary conditions a little faster than 
one-thousandth of an inch per second. 

274. Grotthus' Theory. — We have already mentioned (Par. 195) 
that no signs of the moving ions can be seen between the electrodes. 
Grotthus in 1805 attempted to explain this by the theory that 
there was an exchange of hydrogen atoms from molecule to mole- 
cule of the acid between the electrodes, just as each individual in a 
bucket chain at a fire passes a bucket to the person on one side 
of him and receives a bucket from the person on the other side. 
The correct explanation is that so long as these ions carry charges 
they do not possess their ordinary properties and do not aggregate 
into visible masses. 

275. Electrolytes and Non-Electrolytes. — In Par. 267 we saw 

that solutions of all the acids, all the bases, and all the salts, and 
only these, produce osmotic pressures in excess of those called for 
by theory. From what has been brought out in the preceding 
pages, the student will now be prepared for our final and most 
startling generalization, namely, those and only those solutions 
which produce abnormal osmotic pressure conduct electricity or 
are electrolytes. All other solutions are non-conductors or non- 
electrolytes. 

276. Electrolytic Properties Depend Upon Ionization. — Since 
the common property of these solutions, excessive osmotic pres- 
sures, has been shown to result from ionization, it is but natural 
to assume that their electrolytic property has the same cause. A 
vast accumulation of facts points to this same conclusion. 



210 ELEMENTS OF ELECTRICITY. 

Sulphuric acid when free from water is a non-conductor. Per- 
fectly pure water is also a non-conductor. Such water never 
exists in nature and perhaps may never be prepared, but by a 
special treatment to remove dissolved gases, and a final distillation 
in vacuo, water has been prepared of such purity that a column 
of it one millimeter (one twenty-fifth of an inch) long had the 
same resistance as a copper wire of the same diameter but en- 
circling the earth at the equator 300 times. A solution of sulphuric 
acid in water is, however, a very good conductor. 

Again, since we have seen (Par. 271) that ionization increases 
with dilution, a dilute solution, the amount of dissolved substance 
being kept constant, should conduct better than a strong one, 
and this is found to be the case. 

A solution of hydrochloric acid in water is a very good con- 
ductor; a solution of the same in chloroform, no ionization taking 
place, is a non-conductor. Such examples may be multiplied 
indefinitely. 

277. Vapor Tension. — In Par. 259 illustrations were given of 
the force or pressure which causes gases to diffuse through space, 
and dissolved substances to spread through unoccupied solvent. 
This tendency to diffuse is general. If a liquid be introduced 
beneath a bell jar, a portion of the liquid passes into a state of 
vapor and fills the jar and the evaporation continues until the 
pressure of the vapor above the liquid balances the force which 
tends to throw off the liquid into space. To this force the name 
vapor tension has been applied. It is to be noted that in order to 
pass from a liquid to a vapor a certain amount of heat must be 
taken in by the vapor. The vapor passes off accompanied by this 
latent heat which is necessarily lost by the liquid left behind. 

278. Solution Tension. — Nernst advanced the theory that a 
similar state of affairs obtains for solids immersed in liquids, that 
is, there is a force, designated by him solution tension, which tends 
to drive particles of the solids off into solution in the liquid. We 
have seen (Par. 270) that a metallic ion can go into solution only 
when it carries with it a positive charge. Therefore, parallel to 
the heat in the case of the vapor, the liquid about a metallic plate 
becomes positively charged and the plate becomes correspond- 
ingly negatively charged. Ions continue to be thrown off from the 
metal until the force throwing them off, or the solution tension, 



VOLTAIC ELECTRICITY. 211 

is just counterbalanced by the contrary force of attraction which 
tends to pull the positively charged ions back to the negatively 
charged plate. To this theory the objection was advanced that 
if a metal plate threw off ions it would lose weight but in many 
cases no such loss can be detected by even the most delicate 
measurements. The reply to this is that the quantity of elec- 
tricity carried by the ions is so great that equilibrium is reached 
long before there passes into solution enough ions to be detected 
by our most refined methods of weighing. For example, to carry 
into solution 31.8 grams of copper would require 96,540 coulombs 
(Par. 231) and to carry in only one- thousandth of a gram (the 
smallest amount that can be weighed in an ordinary analytical 
balance) would require over three coulombs, each of which is 
about three billion electrostatic units (Par. 228). 

279. Theory Applied to the Simple Cell. — Consider the case 
of the simple cell (Par. 193). Both the zinc and the copper throw 
off ions into the electrolyte but the zinc has the greater tendency 
to pass into solution therefore more zinc ions go into solution and 
the zinc plate becomes more negatively charged than the copper 
plate. The result is that, as compared to the zinc plate, the 
copper plate is positively charged. When these plates are con- 
nected through the external circuit, the current flows from the 
copper to the zinc, the negative charge on the zinc is partly neu- 
tralized and the zinc plate can therefore throw more ions into 
solution, and so on. 

280. Atomic Character of Electricity. — We have seen above 
that the passage of a given quantity of electricity through an 
electrolyte always releases equivalent weights of ions. Since 
96,540 coulombs liberate one gram of hydrogen and 107.9 grams 
of silver, and since this ratio is constant no matter how many 
coulombs flow through the electrolyte, the quantity of electricity 
that would release one microcrith of hydrogen would also release 
107.9 microcriths of silver, that is, the quantity that releases one 
atom of hydrogen releases one atom of silver and one atom of any 
other univalent element. Since the quantity of electricity which 
releases an ion is equal to the charge which the ion carries, we see 
that all univalent ions carry equal charges, either positive or 
negative. Bivalent ions carry twice the charge of univalent ions. 
and trivalent ions carry three times this charge, and so on. Every 



212 ELEMENTS OF ELECTRICITY. 

unit of valency therefore is accompanied by the same definite 
quantity of electricity, either positive or negative, and since there 
are no fractions of these charges and they vary by whole numbers, 
or in simple ratio, Helmholtz concluded that electricity was 
divided into elementary portions or atoms. These electrical atoms 
which accompany ions are what we have called electrons. Assum- 
ing that an ion and an atom of hydrogen are the same, the electron 
has been calculated as 3.4 x 10 -10 electrostatic units. 

281. Extensive Scope of Theory of Electrolytic Dissociation. — 

The scope of the theory of electrolytic dissociation is extensive. 
Its applications to pure chemistry are even more wonderful than 
those that we have just considered. It explains why water is one 
of the products of most chemical reactions; why the majority do 
not take place unless water be present; why, for example, dry 
sulphuric acid has no effect upon blue litmus; why dry hydro- 
chloric acid does not react with dry ammonia; why dry sulphuric 
acid does not attack dry sodium. It also explains such facts as 
why silver chloride is precipitated by the soluble chlorides yet 
not by the chlorates; why KOH precipitates metallic hydroxides 
yet CH 3 OH does not, etc., etc. The statement is even made, 
though not yet universally accepted, that no metathetical reaction 
is possible unless preceded by ionization either by solution, by 
fusion, or by vaporization. It is being developed by many inves- 
tigators and there is every reason to believe that remaining ob- 
jections which may be advanced against it will shortly be explained 
away. 



VOLTAIC ELECTRICITY. 



213 



CHAPTER 24. 



RESISTANCE. 



282. Resistance. — For the beginner it is helpful in forming a 
physical conception of certain electrical phenomena to think of 
electro-motive force as a pressure which drives or pushes, or tends 
to drive or push, electric charges. If two points between which 
there exists a difference of potential be connected by a conductor, 
the electro-motive force will cause a flow of electricity from the 
point of higher potential to that of lower, and the greater the 
difference in potential between the two points the greater the 
pressure and the greater the quantity of electricity that will flow 
across in a given time. This movement is also affected by the 
nature of the conductor between the two points. For example, 
it takes a longer time for a given quantity of electricity to flow 
through a long thin wire than it does through a short thick one. 
We have seen (Par. 228) that the current is measured by the 
quantity of electricity flowing past a given point in a unit of time, 
hence the current in the long thin wire is smaller than that in the 
short thick wire. The long thin wire therefore cuts down or 
reduces the current by obstructing its flow. This hindrance 
which the wire offers to the flow is called its resistance. 

283. Example of Effect of Resistance. — The following experi- 
ment will show the effect of resistance. Fig. 119 represents 
diagrammatically a cell or battery A and in the external circuit 

B c 




Fig. 119. 

two copper voltameters D and E. When the key K is closed the 
current from the cell divides at B, a part going through the upper 



214 ELEMENTS OF ELECTRICITY. 

voltameter D, and the remainder through the lower voltameter E. 
The electro-motive force which drives the current through the 
two voltameters is precisely the same, since it is due to the dif- 
ference of potential between B and C, but in the upper voltameter 
it has to drive it through the short stout wire and in the lower volt- 
ameter it has to drive it through the longer and thinner wire. If 
the key be kept closed for a convenient time and then opened and 
the cathodes be weighed, it will be found that the cathode of D 
has increased considerably more in weight than that of E, hence 
a greater quantity of electricity has passed through D in the given 
time, that is, the current through D has been greater than that 
through E. 

284. The Practical Unit of Resistance, the Ohm. — This sub- 
ject was investigated first by Ohm who showed that the resistance 
of a given conductor of uniform cross-section varies directly as 
its length and inversely as the area of its cross-section. At the 
time when he carried on his researches there were no units of 
resistance and he therefore extemporized standards by means of 
definite lengths of wire of a given size which, for the sake of com- 
pactness, he wrapped up into coils. He used these resistance coils 
himself and distributed others among those of his scientific friends 
who wished to verify his results. 

The practical unit of resistance, the ohm, is named in his honor 
and will be defined later (Par. 291) ; for the present we must con- 
tent ourselves with the statement that it is about the resistance 
of a piece of ordinary iron telegraph wire, one-sixth of an inch in 
diameter and one hundred yards long; or about the resistance of 
ten feet of annealed copper wire one-hundredth of an inch in 
diameter. 

285. Laws of Resistance. — We saw above that Ohm showed 
that the resistance of a conductor of uniform cross-section varies 
directly as its length and inversely as the area of its cross-section. 
He also showed that it depends upon the material of which the 
conductor is composed. If R represent the resistance of such a 
conductor, this law may be expressed 

R = l - P 

in which I is the length of the 
conductor, s is the area of its cross-section, and p is a factor 



VOLTAIC ELECTRICITY. 215 

depending upon the material and called its specific resistance. 
Resistance also varies with the temperature of the conductor. 

In addition to the foregoing, there are a few substances whose 
resistance varies under certain conditions in an anomalous man- 
ner. For example, when bismuth is placed in a magnetic field its 
resistance increases; when selenium is exposed to light its resist- 
ance decreases. The resistance of some substances, notably 
carbon, decreases with pressure. The prime factors of the resist- 
ance of a conductor, however, are length, area of cross-section, 
material and temperature and these we shall now consider in 
detail. 

286. Resistance Varies Directly with Length of Conductor. — 
This statement requires no amplification. The principle has 
numberless applications. By measuring the resistance of a foot 
of a given wire we can easily calculate the resistance of any speci- 
fied length of it. To determine the length of a submarine cable 
coiled upon a reel, it is not necessary to unwind it. We measure 
its total resistance, obtain by measurement or from a table the 
resistance of the wire per foot, whence we get at once the total 
number of feet. 

If conductors of different lengths, cross-sections or materials 
be connected one after the other, or in series, the total resistance 
of the resulting conductor is the sum of the separate resistances. 

287. Resistance Varies Inversely as Area of Cross- Section of 
Conductor. — The resistance of a conductor varies inversely as the 
area of its cross-section, that is, the greater this area, the less the 
resistance and the less this area, the greater the resistance. For 
the usual current electricity it is unaffected by the geometrical 
shape of the cross-section, and whether this be circular or square 
or irregular or tube like, if the area be the same the resistance is 
the same. The resistance of a wire cable of many strands is the 
same as that of a single conductor whose cross-section is equal to 
the sum of the cross-sections of the separate strands. Since wires 
are usually circular in cross-section, the resistances of equal 
lengths of wire of the same material are to each other inversely as 
the squares of the diameters of the wires. 

28S. Specific Resistance. — If in the expression (Par. 285) for 
the resistance of a conductor 

R = - p 



216 ELEMENTS OF ELECTRICITY. 

we make I = one centimeter and s = one square centimeter, we have 

R = p 

■ But p is the specific resistance of the material of which the 
conductor is composed, whence we see that this specific resistance 
is measured by the resistance of a centimeter cube of the substance 
or of a prism or cylinder whose cross-section is one square centi- 
meter and whose length is one centimeter. The resistance of a 
piece of metal of this size is so small that it is usually expressed 
in millionths of an ohm, or microhms. For example, the specific 
resistance of silver, which is the least, is about 1.5 microhms, that 
of copper about 1.6, that of brass about 7, that of wrought iron 
10 to 15, that of lead about 20, that of mercury about 95, that of 
cast iron over 100. On the other hand, the specific resistance of 
the ordinary electrolytes runs from 1 to 30 ohms while the specific 
resistance of lead glass is given as 84 trillion ohms and that of 
flint glass is two hundred thousand times greater. 

289. Variation of Resistance with Temperature. — The resist- 
ance of ail substances changes as their temperature varies. The 
resistance of the metals increases as their temperature rises; on 
the other hand, the resistance of electrolytes and of most non- 
metals decreases with increase in temperature. This is of especial 
importance in the case of carbon. The resistance of the carbon 
filament in an incandescent lamp when hot and giving light is 
very nearly, if not quite, fifty per cent less than when cold. 

The amount of change in resistance per ohm per degree is 
called the temperature coefficient. The metals therefore have a 
positive temperature coefficient; the non-metals and electrolytes 
have a negative coefficient. Starting at 0° C, the resistance of 
many metals decreases about 2 V 3d for every drop of 1° C. At this 
rate their resistance would entirely vanish at —273° C, which is 
the absolute zero of temperature as deduced from Charles' law of 
gaseous pressure. It is interesting to find this significant tempera- 
ture thus indicated by an independent deduction. It must be 
noted however, that recent experiments show that at the tempera- 
ture of liquid air the resistances no longer decrease at the same 
rate. 

It is highly desirable that we should be able to prepare standards 
of resistance which would be independent of temperature, and 
certain alloys have been discovered whose temperature coefficient 



VOLTAIC ELECTRICITY. 217 

is so small that for most purposes it may be neglected. Typical 
of these is manganin, composed of 84 parts copper, 4 parts nickel 
and 12 parts manganese. 

290. The Platinum Thermometer. — This change of resistance 
with temperature is utilized in the construction of certain forms 
of pyrometers, thermometers for the measurement of temperatures 
beyond the range of the mercurial thermometer or extending up 
to 1000° C. In most of these a platinum wire is wrapped around 
a slender tube of mica which is then slipped into an outer tube of 
fire-resisting porcelain closed at one end. The free ends of the 
wire are brought out of the other end and arranged for attachment 
to a resistance-measuring instrument which may be at some dis- 
tance. The porcelain tube is then inserted into an opening in the 
walls of the furnace or dipped into the molten metal whose tem- 
perature is to be determined. When the coil has attained the 
temperature of the surrounding medium, the resistance of the wire 
is measured by means to be described later (Chap. 26) and the 
corresponding temperature is given by reference to a table or is 
sometimes read directly from a scale which is a component part 
of the apparatus. 

291. The Ohm Defined in Terms of a Column of Mercury. — 

The comparisons in Par. 284 are only crude approximations and 
can hardly be made anything more, for the resistance of iron and 
of copper varies greatly with even slight traces of impurities and 
with the temper and annealing. Mercury is a metal which by 
simple distillation and washing is readily obtained in a high state 
of purity; it is also free from the troubles of tempering and anneal- 
ing and finally its resistance is nearly sixty times greater than that 
of copper. The apparent disadvantage of not being able, on ac- 
count of its liquid state, to obtain it in wires is easily overcome 
by pouring it into glass tubes of the required size, and electric 
connection with it is made by simply dipping into it the conducting 
wires. The International Congress of Electricians in Chicago in 
1893 (Pars. 212, 232) defined and recommended that there be 
adopted "as a unit of resistance, the International Ohm . . . repre- 
sented by the resistance offered to an unvarying electric current 
by a column of mercury at a temperature of melting ice, 14.4521 
grammes in mass, of a constant cross-sectional area and of the 
length of 106.3 centimeters." This corresponds to a cross-section 



218 ELEMENTS OF ELECTRICITY. 

of one square millimeter but the weight of the mercury is given 
instead of the diameter of the tube since, of the two, the weight 
is the more easily and accurately measured. 

292. Resistance and Conductance. — The terms resistance and 
conductance are reciprocals. The less the resistance of a conductor, 
the greater its conductance; the greater its resistance, the less its 
conductance. The unit of resistance is the ohm. There is no 
need for a unit of conductance yet it has been given a name, the 
mho (the word ohm backwards). A body whose resistance is 
three ohms has a conductance of one- third mho. 

There is no conductor devoid of resistance; so also there is no 
absolute non-conductor. Substances may be arranged in order of 
their relative conductance or, as it is frequently called, their 
conductivity, this being the reciprocal of specific resistance, also 
called resistivity. Silver is the best conductor and copper comes 
next. Conductivity is expressed in percentage, that of annealed 
copper being taken as 100 since copper and not silver is the stand- 
ard material for electric wiring. The following table gives the 
conductivity of the commoner metals as determined by Fleming 
and others. 

Metal Conductivity- 
Silver, pure 108.60 

Copper, annealed 100 . 00 

Gold 97.80 

Aluminum 63.00 

Zinc 27.72 

Brass 22.15 

Iron, wrought, average 15 . 00 

Steel 11.60 

Lead 7.82 

German Silver 5 . 32 

Mercury 1 . 69 

293. Resistance of Conductors in Parallel. — If an electric 
circuit splits into two or more portions which again unite, it is 
called a divided circuit. Such a circuit of three branches is repre- 
sented in Fig. 120. The three branches are said to be in parallel. 
A turnout which enables cars travelling at different speeds, or in 
opposite directions on a single track, to pass each other is some- 
times called a shunt. From analogy, any branch of a divided 



VOLTAIC ELECTRICITY. 219 

circuit may be called a shunt for the remaining branch or 
branches. 

It frequently becomes necessary to determine the resistance of 
a divided circuit, that is, the joint resistance of two or more con- 
ductors in parallel. Suppose we have in parallel two wires, one of 

A 



7 



Fig. 120. 

ten ohms and the other of one ohm resistance; what is their joint 
resistance? The tendency for a beginner is to say the average of 
the two, but reflection will show that the two wires side by side 
are equivalent to a single wire of greater cross-section and hence of 
less resistance than either. In other words, the joint resistance 
of any number of resistances in parallel is always less than that 
of the least. 

Joint resistance may be determined as follows: If A, B and C 
be the resistances of the branches in Fig. 120, their conductance 

is -j> -^ and p. Their joint conductance is the sum of the 

separate conductances or 

III 1 - AB + AC + BC 
A + B + C ABC 

Their joint resistance is the reciprocal of this or 

■R = ABC 

AB + AC + BC 

and in general the 
joint resistance of any number oj resistances in parallel is the 
reciprocal of the sum of the reciprocals of the separate resistances. 
If there be but two resistances, the formula becomes 

F AB 

or the joint resistance is 
the product of the two divided by their sum. 

Should A, B and C be equal, the expression becomes 

A 



*-3 



and in general the joint 



220 ELEMENTS OF ELECTRICITY. 

resistance of any number of equal resistances in parallel is equal to 
that of a single resistance divided by the number in parallel. 

294. Internal Resistance of Cells. — In the employment of 
voltaic cells as a source of electrical energy, the question of their 
resistance is of great importance. In Par. 288 we saw that while 
the specific resistance of copper is about 1.6 microhms (millionths 
of an ohm), that of the usual electrolytes runs from 1 to 30 ohms, 
that is, the resistance of the electrolyte is on an average 10,000,000 
times greater than that of the copper. This resistance, spoken of 
as the internal resistance of the cell, follows the same laws as other 
resistances (Par. 285). With a given electrolyte, we may reduce 
the internal resistance of a cell in two ways. First, by bringing the 
plates of the cell closer together we may shorten the path which 
the current has to follow. Second, by increasing the area of the 
plates we increase the number of available paths for the current, 
or increase the cross-section of the total path. A thin sheet of 
copper parallel and close to the zinc plate offers far less resistance 
than the same mass of copper in a more compact form. As the 
zinc and copper plates are flattened out and increased in size the 
glass cell must keep pace, but as it gets larger it increases rapidly 
in cost. Reflection will show that two cells in parallel are elec- 
trically equal to a single cell with plates twice as large. Therefore, 
the usual method of increasing the cross-sectional area of a 
battery is to join cells in parallel. 

295. Wire Tables. — As the practical electrician has to deal 
largely with wires, it is important that he should possess infor- 
mation as to the different sizes, their dimension, weight, resistance, 
etc. Such data is embodied in wire tables which are issued by the 
wire manufacturers and are also found in the various electrical 
hand-books. The sizes of wire are designated by numbers corre- 
sponding to certain wire gauges. It is unfortunate that there are 
in existence four or five of these gauges and that their numbers 
do not correspond nor do their sizes of wire vary in accordance 
with any fixed rule. In this country the gauge in most common 
use is the American wire gauge of the Brown and Sharpe Company. 
The Birmingham wire gauge is also in use. The No. 1 wire on the 
Brown and Sharpe gauge is very nearly .3 of an inch in diameter, 
and the smallest wire, or No. 40, is about .003 of an inch. There 
are four sizes larger than No. 1 and they are designated single 0, 



VOLTAIC ELECTRICITY. 



221 



double 0, treble 0, etc. The No. 10 wire on the B. & S. gauge is 
just about .1 of an inch in diameter and if of copper its resistance 
is about one ohm per 1000 feet. As a rule of thumb, by subtracting 
three from the gauge number of any wire we get the number of 
the wire whose cross-sectional area is twice as great. The cross- 
sectional area of No. 7 is twice that of No. 10. 



COPPER WIRE TABLE, BROWN AND SHARPE GAUGE. 

Resistance at 20° C. 



Size of 


Diameter, 


Ohms per 


Feet per 


Pounds per 


wire 


inches 


foot 


ohm 


foot 


0000 


0.460 


0.00004893 


20,440 


0.6405 


000 


0.4096 


0.00006170 


16,210 


0.5080 


00 


0.3648 


0.00007780 • 


12,850 


0.4028 





0.3249 


0.00009811 


10,190 


0.3195 


1 


0.2893 


0.0001237 


8,083 


0.2533 


2 


0.2576 


0.0001560 


6,410 


0.2009 


3 


0.2294 


0.0001967 


5,084 


0.1593 


4 


0.2043 


0.0002480 


4,031 


0.1264 


5 


0.1819 


0.0003128 


3,197 


0.1002 


6 


0.1620 


0.0003944 


2,535 


0.07946 


7 


0.1443 


.0.0004973 


2,011 


0.06302 


8 


0.1285 


0.0006271 


1,595 


0.04998 


9 


0.1144 


0.0007908 


1,265 


0.03963 


10 


0.1019 


0.0009972 


1,003 


0.03143 


11 


0.09074 


0.001257 


795.3 


0.02493 


12 


0.08081 


0.001586 


630.7 


0.01977 


13 


0.07196 


0.001999 


500.1 


0.01568 


14 


0.06408 


0.002521 


396.6 


0.01243 


15 


0.05707 


0.003179 


314.5 


0.009858 


16 


0.05082 


0.004009 


249.4 


0.007818 


17 


0.04526 


0.005055 


197.8 


0.006200 


18 


0.04030 


0.006374 


156.9 


0.004917 


19 


0.03589 


0.008038 


124.4 


0.003899 


20 


0.03196 


0.01014 


98.66 


0.003092 


21 


0.02846 


0.01278 


78.24 


0.002452 


22 


0.02535 


0.01612 


62.05 


0.001945 


23 


0.02257 


0.02032 


49.21 


0.001542 


24 


0.02010 


0.02563 


39.02 


0.001223 


25 


0.01790 


0.03231 


30.95 


0.0009699 


26 


0.01594 


0.04075 


24.54 


0.0007692 


27 


0.01420 


0.05138 


19.46 


0.0006100 


28 


0.01264 


0.06479 


15.43 


0.0004837 


29 


0.01126 


0.08170 


12.24 


0.0003836 


30 


0.01003 


0.1030 


9.71 


0.0003042 



222 ELEMENTS OF ELECTRICITY. 

296. Circular Measure of Wires. — Owing to the errors likely 
to occur from lack of agreement in the sizes of the various wire 
gauges, it is becoming more and more the custom among elec- 
tricians to designate wires by their diameters expressed in thous- 
andths of an inch or mils, indeed, by recent orders of the War 
Department this has been made mandatory for our army. If we 
compare the area of cross-section of a wire whose diameter is one 
mil with that of one whose diameter is n mils we see, since the 
areas of circles are to each other as the squares of their diameters, 
that the cross-section of the larger wire is n 2 times greater than 
that of the smaller. Because of this very simple relation, the area 
of cross-section of a wire of one mil diameter is taken as the unit 
of area and called a circular mil. To find the area in circular mils 
of the cross-section of any other wire we simply square its diameter 
expressed in thousandths of an inch. This method of comparison 
is very much simpler than expressing the cross-sections in square 
inches. A piece of wire one foot long and one mil in diameter is 
called a mil foot. The resistance of a mil foot of annealed copper 
is 9.59 ohms at 32° F and 10.505 ohms at 75° F. With this data 
we may, by applying the law given in Par. 287, determine the 
resistance of a copper wire of any size and length. 



VOLTAIC ELECTRICITY. 223 



CHAPTER 25. 

OHM'S LAW. 

297. Ohm's Law. — As a result of his investigations, Ohm 
announced in 1827 the law which bears his name and which is to 
the effect that in any electric circuit the current varies directly 
as the electro-motive force and inversely as the resistance of the 
circuit. Expressed in symbols this becomes 

1 = 1 

1 R 

in which, if E be the E. M. F. in 
volts and R the resistance in ohms, I is the current in amperes. 

In its determination Ohm employed the rather crude appliances 
which he extemporized for the purpose (Par. 284). Since his time 
the delicacy and accuracy of electrical apparatus have been 
immensely increased, yet the most careful and refined observations 
serve merely to afford stronger confirmation of his conclusions. 

The importance of this law can not be over-estimated. In the 
study and application of electricity it is fundamental and in one 
form or another it is met at every turn. On account of its very 
simplicity there is sometimes a failure to recognize that it is 
unique, and occasionally it is spoken of as "self evident." Such 
is far from being the case. There is no material substance which 
follows such a law. Pressure causes liquids and gases to flow 
through pipes, yet if this pressure be doubled the flow is by no 
means doubled. 

When applying the law to a more or less complex circuit, E 
represents the total E. M. F. and R the total resistance. Thus there 
may be several cells or batteries or electrical machines contrib- 
uting to the E. M. F., in which case the sum of the E. M. F.s 
must be taken. Again, through error or by design a cell or battery 
may be reversed so as to oppose the remaining E. M. F. Such 
opposing E. M. F. is spoken of as counter E. M. F. or back E. M. F. 
Back E. M. F. is also produced by polarization (Par. 198") and. 
as we shall see later, by the operation of motors in the circuit. In 



224 ELEMEXTS OF ELECTRICITY. 

summing up the total E. M. F. of the circuit, back E. M. F. is to 
be considered as negative. The resistance R includes not only 
the resistance of the line but also that of the contacts, joints and 
connections and of the electrolyte and elements of the cells. The 
law can therefore be given 

E' + E" + E'" + E"" + &c. 

R' + R" + R'" + R n " + &c. 

or the current 
in the circuit is equal to the algebraic sum of the separate 
E. M. F.s divided by the sum of the separate resistances. 

298. Drop of Potential. — The three quantities, current, electro- 
motive force and resistance are bound together by Ohm's law so 
that any two being given, the third may be determined. It may 
at first sight appear unnecessary to state such a self-evident truth 
but it is desirable to lay especial emphasis upon the fact for, until 
the student has become familiar with the law, the tendency is 
rather to restrict its use to the determination of current only. 

The law may be put in the form 

E = IR 

and it is helpful to the 
beginner if he wall accustom himself to interpret this as meaning 
that E is the electro-motive force necessary to drive a current 
of strength I through a resistance R. 



JD' 



i 
i 
i 

i 
i 



Fig. 121. 

Suppose AB (Fig. 121) to represent a portion of an electric 
circuit, the point A being of higher potential than B, and suppose 
that by means of one of the instruments to be described later 
(Chapter 34) we measure the difference in potential between 
A and B. Lay off on some convenient scale A A' proportional 
to this difference of potential. If we move along AB to some 
point D and measure the difference of potential between D and B 



VOLTAIC ELECTRICITY. 225 

we will find it to be less than that at A, or represented by DD'. 
Likewise, at F this difference of potential is still smaller and is 
proportional to FF', that is, as we move from A towards B the 
difference of potential between the successive points and B 
steadily grows less, or there is a falling off from the difference of 
potential represented by A A'. At D, for example, this drop of 
potential is D"D' and at F it is F"F'. 

The drop of potential between any two points is always equal 
to the product of the current into the resistance between the points. 
Certain elementary applications of this principle will be shown 
in the following paragraphs. 

299. Ohm's Law Applies to Any Portion of the Circuit. — In Par. 

297 we saw that Ohm's law was applicable to the entire circuit 
even though this be made complex by including heterogeneous 
resistances and sources of E. M. F. It also applies to any portion 
of a circuit, that is, the current flowing between any two points 
in a circuit is equal to the difference of potential between these 
two points divided by the resistance between them. We have seen 
(Par. 229) that the current at every cross-section of a circuit is the 
same; if, therefore, we determine it at one point we have it for 
any other point. Knowing the current, if we have the resistance 
between two points we can, by what we have shown in the pre- 
ceding paragraph, determine the difference of potential, or drop, 
between the two points. These principles enable us to solve a 
variety of problems. For example, let ABCD, Fig. 122, repre- 
sent part of an electric circuit. The resistance of the portion AB is 
12 ohms, that of the incandescent lamp BC is 220 ohms, that of 
CD is 8 ohms. The difference of potential between A and B is 6 
volts. What current is flowing in the circuit and what is the poten- 
tial of the points A, B and C if that of D be taken as zero? 



12, OHMS 



8 OHMS 




220 OHMS 



F fi 1 

The current between A and B = -^ = =75. = s ampere, which is 

tc 1Z z 

also the current for the rest of the circuit. The drop from B to C = 



226 



ELEMENTS OF ELECTRICITY 



IR = \ X220 = 110 volts; that from C to D = \ X8 = 4 volts. The 
potential of C is therefore 4 volts, that of B is 114, and that of A 
is 120. 

300. Division of Current in Divided Circuit. — This principle of 
drop of potential furnishes a simple determination of the division 
of an electric current in a divided circuit. 



I 



R' 



B 



Fig. 123. 

Let Fig. 123 represent a divided circuit of three branches whose 
resistances are respectively R', R" and R'" . Call the correspond- 
ing currents /', I" and T" . The current in the main branch upon 
arriving at A divides into these three portions which reunite at B. 
The drop from A to B is the same over each of the three routes, 
therefore 

I'R'=I"R n =I'"R'" 

which may be written 

Ji . jn . Tin __ jj^_ . -*- . -L 

' " R' ' R" ' R'" 

that is, the current 
in the branches of a divided circuit are to each other inversely as the 
resistances of the respective branches. 

In making an actual calculation, if the fractions in the second 
member of this proportion be brought to a common denominator, 
their numerators indicate at once the relation between the several 
currents. 

If there be but two branches, the above becomes 



I' - I" = -— 
11 R' 



J, 
R' 



which may be written 



form for calculations. 



/' :I" = R" :R' 



a somewhat simple 



301. Shunts.— In practical electricity it frequently becomes 
necessary to employ a divided circuit of two branches which must 



VOLTAIC ELECTRICITY. 227 

be so proportioned that the main current divides between them 
in accordance with some desired ratio. For example, suppose that 
we wish to measure a current which is much larger than can be 
measured directly by the instruments at our disposal. If we can 
arrange a divided circuit so that exactly one-hundredth of the 
total current flows through one branch, we can measure this 
small current and always know that the entire current is one 
hundred times greater. This division is brought about by shunts 
(Par. 293). 

In Fig. 124 we desire to measure the current flowing in AD. 
G is our measuring instrument which with its connecting wires 
BG and GC has a resistance of R ohms. BC is the shunt. What 
must be the resistance of the shunt so that one-hundredth of the 
total current will flow through G ? 




B/___\c 
— cy/////////////////m 



Fig. 124. 

Call the current through the instrument I; that through BC 
will be 997. If x be the resistance of BC, then, as shown in the 
preceding paragraph 

I XR = 991 Xx 

whence _ R_ 

X "99 

or the resistance of the shunt 
must be one-ninety-ninth of the resistance of G and its connecting 
wires and leads. In a similar manner we can determine the 
resistance of shunts to bring about division of the total current in 
any desired ratio. It is to be noted that these shunts are con- 
structed for use with a particular instrument and cannot be used 
with another of different resistance. 

302. Rheostats. — A consideration of Ohm's law, I = E R, will 
show that by varying R we can vary the current inversely and 
suggests that by introducing or removing resistance from a cir- 
cuit we may regulate the current at will. Instruments for this 
purpose are called rheostats. The principle of their use will be 



228 ELEMENTS OF ELECTRICITY. 

understood from the diagram (Fig. 125). A series of metal con- 
tacts are arranged upon the arc of a circle DE and connected 
between these contacts are resistance coils. Pivoted at the center 




of the arc is a metal arm CD which can be moved about over the 
contacts. Suppose the current to come in by A. As represented 
in the figure, it must now traverse all the coils from D to E before 
it can leave by B, and it is therefore cut down. Had the arm CD 
been still farther to the left, the circuit would have been broken 
entirely, R would have been infinite and the current zero. As the 
arm is slid around to E the coils are successively cut out, the 
resistance correspondingly reduced, and the current correspond- 
ingly increased, reaching its maximum when the arm reaches E. 
The controller by which the motorman starts and stops a trolley 
car is similar in principle. 

It will be shown later that regulation of current by rheostat is 
a wasteful method and except for temporary purposes, such as for 
starting and stopping motors, should not be employed. 

303. Kirchoff's Laws. — Where an electric circuit is composed 
of interlacing branches and especially where there are in it several 
seats of electro-motive force, confusion and uncertainty may 
arise as to the correct way of applying Ohm's law in the determina- 
tion of the separate currents and potentials. To obviate this, 
Kirchoff has formulated a set of rules which render this applica- 
tion almost mechanical. These are: 

I. If several conductors meet at a common point, the algebraic sum 
of the currents in these conductors is zero. 

This is but a statement of the fact that electricity does not 
accumulate at a point and that therefore as much flows away as 
flows to the point. If currents flowing to the point be considered 
positive, those flowing away must be regarded as negative. 

II. If two or more conductors form a closed figure, or a mesh in a 
network of conductors, the sum of the products of each current of this 






VOLTAIC ELECTRICITY. 



229 



mesh into the resistance through which it passes is equal to the algebraic 
sum of the electro-motive forces acting around this same mesh. 

This is another statement of the fact, that the total drop of 
potential in going around a closed circuit is equal to the sum of 
the partial drops. The convention must be adopted that in going 
around a closed circuit, if the E. M. F. acting in a clockwise direc- 
tion be considered positive, that acting in the opposite direction 
is negative. 

304. Example of Application of Kirchoff's Laws. — By combin- 
ing these laws it is always possible to obtain as many independent 
equations as there are unknown quantities and hence these 
unknown quantities may be determined. The following concrete 
example will make the matter clear. Fig. 126 represents a net- 
work of conductors in two of the branches of which there are bat- 
teries E and F, sources of E. M. F. The currents in the separate 




branches are designated i u i 2 , is, etc., and their assumed direction 
is indicated by the arrows. In the final solution, a negative value 
of a current indicates that the actual direction is opposite to that 
assumed. The E. M. F. of the batteries and the resistances of the 
branches are indicated on the diagram. We are required to deter- 
mine the currents in the separate branches. 

From KirchofFs first law we obtain the following "point 
equations": 

point a ii — i 2 — % = 

point b ii + * 5 — ii = 

point c i» — u — u = 

point d i- s + ^ 6 — i b = 



230 ELEMENTS OF ELECTRICITY. 

From the second law we obtain the following "voltage 
equations": 

mesh ixi^ii 5ii + 2i 2 + 3i 4 = 3 
mesh izizU 3i 3 — 4:i Q — 2i 2 = 
mesh ui&ie 4i 6 + 4i 5 — 3i 4 = — 2 
mesh ifcib 5ii + 3i 3 + 4i 5 = 3 — 2 

We now have eight equations from which to determine six 
unknown quantities, and the remainder of the process is but a 
matter of combination and elimination. 

305. Lost Volts and Useful Volts. — Should there be connected 
up to a circuit of resistance R a cell whose E. M. F. is E and in- 
ternal resistance r, the resulting current would be given by the 
expression 

R + r 
which may be written 

E = IR + Ir 

Interpreting this as explained in Par. 298, we see that a part of 
the E. M. F. of the cell is spent in driving the current through the 
external resistance R and the remainder in driving this current 
through the internal resistance of the cell. The volts, Ir, con- 
sumed on the interior of the cell are called the lost volts and we 
profit only by those upon the external circuit, or IR, which are 
therefore called the available or useful volts. Since the less the lost 
volts, the more the useful volts, it is of importance to keep the 
former at a minimum. Ir may be reduced in two ways; by reduc- 
ing the current or by decreasing the internal resistance. If there 
be no current, there is of course no wastage. The internal resist- 
ance may be reduced by selecting an electrolyte of low resistance 
(though usually choice is restricted), by bringing the plates closer 
together, and by increasing the size of the plates (Par. 294). Lost 
volts have also to be considered in the operation of electrical 
machinery. 

306. Short Circuit. — The commonest source of injury to elec- 
trical machinery is a short circuit, which may be defined as the 
removal, usually accidental, of the greater part of the resistance 
from a "live" circuit, (one in which there is E. M. F.). 



VOLTAIC ELECTRICITY. 231 

Suppose B (Fig. 127) to represent a battery supplying current 
for the incandescent lamp L. The internal resistance of the bat- 
tery is almost negligible, the resistance of the wires should be very 



5 



Fig. 127. 

small. Suppose the E. M. F. of the battery to be 111 volts, the 
resistance of the lamp to be 220 ohms and that of the battery 
and wires to be 2 ohms. The current is 

111 1 

1 = 220+^ = 2 ampere 

If by some accident the wire should sag, as shown by the dotted 

line, and touch the lower wire at P, at that instant the current 

would be short circuited through the point P, the resistance of the 

lamp and of the wire beyond P being eliminated. The current is 

now HI 

I = -y- = 111 amperes 

or it has suddenly in- 
creased over two hundred times. If the wires had been designed 
to carry only ten or fifteen amperes they will be fused, apparatus 
in the circuit will be "burned out," insulation will be charred and 
possibly fires started. To avoid the injury resulting from such 
accidents, use is made of fuses, pieces of soft, easily-fusible wire 
inserted in the circuit which is to be protected. If the current 
exceeds that which the fuses are intended to carry, they melt 
before damage is done to the rest of the circuit. This same pro- 
tection is also afforded by certain automatic apparatus called 
overload switches (Par. 414). 

307. Definitions Based Upon Ohm's Law. — Since the three 

quantities /, E and R are bound together by Ohm's law, any one 
may be defined in terms of the other two. Thus the ampere is 
sometimes defined as the current produced by an E. M. F. of one 
volt applied to a conductor whose resistance is one ohm. So also 
the volt is defined as that E. M. F. which applied to a resistance of 
one ohm will produce in it a current of one ampere. The ohm may 



232 ELEMENTS OF ELECTRICITY. 

be similarly defined but such definition adds but little to our 
knowledge. 

Since Ohm's law may be written 

«-? 

and since E and / fluctuate 
together so that R remains always constant, the resistance of a 
conductor is defined by some writers as the ratio of the difference 
of potential of the ends of the conductor to the current produced 
in it. To define a property as a ratio is not altogether satisfactory. 
It is perhaps better to say that this ratio affords a measure of the 
resistance. 






VOLTAIC ELECTRICITY. 233 



CHAPTER 26. 
MEASUREMENT OF RESISTANCE. 

308. Measurement of Resistance. — One of the most important 
classes of measurements with which the electrician has to deal is 
that of resistance. Logically, this subject should have been taken 
up in connection with that of resistance in Chapter 24, but the 
methods employed could not be clearly presented until after the 
consideration of Ohm's law and the explanation, as given in Chap- 
ter 25, of the principles of the drop of potential and the division 
of current in a divided circuit. Even now we shall have to antici- 
pate certain principles which can not be fully developed until 
later. 

In these measurements, the methods to be employed vary with 
the amount and character of the resistance. Thus, very high and 
very low resistances are measured in a different way from those 
covering a moderate range. Again, the measurement of the in- 
ternal resistance of cells and of the resistance of electrolytes must 
be undertaken in an entirely different manner from that of a 
metallic conductor. These facts will be brought out in the follow- 
ing pages. 

309. Drop of Potential Proportional to Resistance Passed 
Over. — If there exists between AB (Fig. 128), two points of a cir- 




cuit, a difference of potential E, there will be a flow of electricity 
from the point of higher potential to that of lower. The value of 
this current as given by Ohm's law is I = E/R, whence E = IR, 
which last expression, as we have already seen (Par. 298), may be 
interpreted as expressing the fact that E is the electro-motive 
force required to drive a current of strength / through the con- 
ductor of resistance R. 



234 ELEMENTS OF ELECTRICITY. 

To drive the same current through a resistance only one-half as 
great requires only one-half as much E. M. F., or, if the resistance 
of AM be one-half of the total resistance between A and B, then 
one-half of the total E. M. F. will be expended in driving the cur- 
rent from A to M, and the difference of potential between M and 
B is only one-half of that between A and B. In more general 
terms, for a constant current, the expenditure of E. M. F., or the 
drop of potential, is directly proportional to the resistance passed 
over. 

310. Measurement of Resistance by Drop of Potential. — 

Should we have at our disposal a known resistance and an instru- 
ment for measuring difference of potential (Chapter 34), the fore- 
going affords us a means of measuring the resistance between any 
two points in a circuit. For example, suppose that the resistance 
R between A and M, Fig. 128, be known and that we desire to 
determine the resistance x between M and B. We have simply 
to measure with our instrument the drop E' between A and M, 
and the drop E" between M and B. From the preceding paragraph 

E' :E" = R :x 

whence x = -^ R 

This method supposes the current to be constant during the two 
observations; the battery should therefore be one of constant 
E. M. F. and the observations should be taken in quick succession 
so as to avoid change in the current due to the increase of the 
resistance of the circuit caused by the heating effect of the current. 

311. Resistance Coils. — The known resistances used as de- 
scribed in the preceding paragraph are usually in the form of coils. 
These resistance coils, especially those used as standards of resist- 
ance, are made with great care and accuracy and embody many 
refinements. They range from .001 of an ohm to 10,000 ohms. 
A section of one is shown in Fig. 129. From the ebonite lid there 
extends downwards a hollow metal cylinder which has an insulat- 
ing covering of shellac-coated silk. Around this cylinder is wrapped 
the coil proper which is of silk-insulated manganin wire (Par. 289). 
For reasons which are explained later (Par. 315), the wire is 
doubled upon itself at its middle point and the winding is begun 
at this loop. The ends of the coil are attached to heavy copper 



VOLTAIC ELECTRICITY. 



235 



terminals bent downward as shown. The coil is connected up in 
the circuit by inserting these turned-down ends into mercury cups 
which in turn are connected to the lead wires. The whole is pro- 




Fig. 129. 

tected by a brass case which is perforated by many small openings. 
The object of the interior metal cylinder is to conduct away heat 
developed in the wire and at the same time to afford a large sur- 
face for radiation. The object of the openings is to allow the 
enclosed coil to cool off more rapidly and also to permit the tem- 
perature to be kept down by submerging the entire coil in oil. 
The plug in the center of the lid is to permit the insertion of a 
thermometer for reading the temperature of the coil so that the 
proper correction for temperature may be applied. 

312. Drop in Divided Circuit. — The usual way of measuring 
ordinary resistances is by means of the Wheatstone bridge, a piece 
of apparatus whose principle will be understood from the following 
explanation. Consider a divided circuit of two branches and let 
A (Fig. 130) be the point of high potential. The current at B 
divides into two parts inversely proportional to the resistances of 
the two branches, i. e., the greater part goes along the branch of 
least resistance, the lesser part along the branch of greater resist- 
ance. There is a continuous drop of potential along each branch 
of the circuit from B to D, in other words, the drop of potential 
over the two branches is exactly the same. Suppose following the 
right hand branch we reach a point M at which we have passed 
over one-half of the resistance in that branch ; the difference of po- 
tential between M and D is only one-half of that between B and D. 



236 



ELEMENTS OF ELECTRICITY. 




Fig. 130. 



Similarly, following the left hand branch and reaching a point 

N at which we have passed over one-half of the resistance in that 
A branch, the difference of potential between 

N and D is only one-half of that between B 
and D. Hence, the points M and N are at 
the same potential. This can be shown by 
connecting between these points a sensitive 
galvanometer G. (Galvanometers are de- 
scribed in Chapter 30. For the present it is 
sufficient for us to know that a galvanometer 
(more strictly a galvanoscope) is an instru- 
ment which indicates by the movement of 
its needle that a current is flowing in the 
circuit of which it forms a part, and by the 
direction of the motion of the needle indi- 
cates the direction of the current.) Should 
there be a difference of potential between M 
and N, a current would be produced and 
would be revealed by a deflection of the gal- 
vanometer needle, but the needle will be found to remain at rest. 
The foregoing illustration is based on the supposition that the 

resistance of BM and of B N are each one-half of the resistance of 

the respective branches, but the prin- 
ciple is equally true for l/wth, that is, 

if the resistance of BM be 1/nth. of 

that of the right hand branch and the 

resistance of B N be 1/nth. of that of 

the left hand branch, the points M and 

N will be at the same potential and 

there will be no flow of current between 

them if they be connected through a 

galvanometer. 

313. Principle of the Wheatstone 

Bridge. — Let us now consider a divided 

circuit of two branches (Fig. 131), 

each branch subdivided into two parts 

as shown, and suppose that in the left 

hand branch we know the resistance 

of A and of R and further can vary that of R at pleasure, and 

that in the right hand branch we know the resistance of the 




Fig. 131. 



VOLTAIC ELECTRICITY 237 

portion B but do not know that of the remainder X and wish to 
determine it. Of the total resistance of the right hand branch, 
X is some definite fraction, say 1/nth. Since R may be varied at 
pleasure, it can be adjusted so that it is 1/nth of the total resist- 
ance in the left hand branch. When such a state of affairs is 
reached, the points M and N will, from what has been shown 
above, be at the same potential and the galvanometer connected 
between M and N will reveal no current. The system is now 
said to be "balanced." 

Since X is 1/nth of the total resistance in the right hand branch, 
B is n — l/nths, and since R has been made 1/nth. of that in the 
left hand branch, A is n — 1/nths. 

Hence A : B : : R : X 

Whence X = — p 

or, when the system has been 
brought to a balance, the resistance in X is equal to the product of 
the resistances in the adjacent arms divided by that of the opposite arm. 

314. A Second Demonstration. — The same thing can be readily 
shown by applying the principle of drop directly. Call the current 
in the left hand branch I ', that in the right hand branch I", and 
the resistance in the four arms A, B, R, and X, respectively. The 
drop from S to N is equal to the current times the resistance or 
TA\ that from S to M is equal to I"B. But M and iV being at 
the same potential these drops are equal. Similarly, the drop 
from N to T, or I'R, is equal to the drop from M to T, or I"X. 

We then have the two equations, 

(I) FA = I"B 

(II) I'R =rx 

Dividing (II) by (I). and striking out common factors 

R_X 
A B 



Whence as above 



X '"A 



The foregoing is the principle upon which the Wheatstone 
bridge is constructed. 



238 



ELEMENTS OF ELECTRICITY. 



The expression X = 



~R~R R 

—7- can be written X = -j R, whence it is 



seen that if B and A be so selected that B/A is some multiple or 
submultiple of ten, calculations will be simplified since all that 
will then be necessary will be to point off decimal places or add 
zeros to the value of the known resistance R. 

315. Arrangement of Resistances. — In the actual apparatus 
the resistance in the arms A, B, and R is usually varied by re- 
moving or changing the position of certain plugs. For example, 




Fig. 132. 

the arm A, a portion of which is represented in Fig. 132, consists 
of a heavy brass bar DE secured to the ebonite plate FF and cut 
entirely through at regular intervals by tapering openings into 
which fit the corresponding ebonite-handled brass plugs A, B, C. 
The separate sections into which the bar is divided are connected 
beneath the plate FF by the resistance coils G, H, K. These are 
wound as described in Par. 311 so as to avoid self-induction. For 
the present we may explain this by stating that when a circuit 
through a coil of wire is completed there is produced through 
induction an opposing E. M. F. which causes the current to lag 
and prevents it from rising to its full strength at once. When a 
coil is made by winding it from a loop at its middle point, each 
turn of the coil carrying a current is paralleled by an equal turn 
in which the current flows in the opposite direction and the 
inductive effects of the two turns exactly neutralize each other. 
These coils have a resistance of 1 ohm, 10 ohms, 100 ohms, etc., 






VOLTAIC ELECTRICITY. 



239 



and therefore bear to each other the ratio of 1 : 10 : 100, etc. 
With the plugs in position the current passes from D to E through 
the bar and coils, the combined resistance of which is so small as 
to be negligible. With the plug B removed, the current must 
follow the path D M H N E, that is, the resistance of the coil 
H has been introduced into the circuit. 

In the arm R the arrangement is similar but there is a much 
greater number of coils whose resistances are in ohms 1, 2, 3, 4, 
10, 20, 30, 40, 100, 200, 300, 400, 1000, 2000, 3000, 4000, etc., thus 
enabling any combination from 1 to 11110 to be obtained. This 
arm is usually called the "rheostat" and is consequently desig- 
nated in diagrams by letter R. 

316. Evolution in Form.— The theory of the Wheatstone 
bridge is best explained as above from a diagrammatic diamond- 








(3) 
Fig. 133. 



(5) 



shaped figure as in (1), Fig. 133. The commercial form of this 
apparatus bears no superficial resemblance to the figure but has 
been evolved directly from it as the following will show. 

1st step. The galvanometer need not be placed in the diamond 
but may be connected outside as shown in (2). 

2d step. A and B need not make an angle with each other 
but may be flattened down as shown in (3). 

3d step. R being the arm which carries the greatest number 
of resistance coils should, relatively to A and B, be elongated as 
shown in (4). 

4th step. Finally, for the sake of compactness, the arm R 
may be folded back upon itself as shown in (5). 

Other minor changes consist in the arrangement of the terminals 
to facilitate connections, and in the insertion in the battery and 



240 



ELEMENTS OF ELECTRICITY. 



galvanometer circuits of keys permanently attached to the instru- 
ment. Sometimes a galvanometer is included in the case. The 
final result is an instrument of which Fig. 134 shows a form made 
by the Leeds & Northrup Co. 




Fig. 134. 



The various circuits between the keys and other parts of the 
bridge are inside the case but are usually indicated by white lines 
marked on the cover. 

317. Connections for a Measurement. — Whatever be the form 
of the bridge it is well to bear in mind the following: — first, the 
current enters (or leaves) at the junction of A and B and leaves 
(or enters) at the junction of R and X; second, the galvanometer 
is connected between the junction of A and R and that of B and X. 
(It should however be observed that it may readily be shown that 
the battery and the galvanometer may be interchanged, the 
resistance of their respective leads altered at will, and the E. M. F. 
of the battery varied, all this without affecting the balance.) 
Finally, in the factor by which R is to be multiplied, the resistance 
of B, the arm connected to X, is the numerator and that of A, 
the arm opposite X, is the denominator. 

318. Operation of Measurement. — To measure the resistance, 
say of a wire X, the apparatus is brushed free from dust, and 
plugs brightened, being especially careful to remove all grease 



VOLTAIC ELECTRICITY. 



241 



or oil so as to insure perfect contacts. Connections are then made 
as shown in Fig. 135. A plug is removed from coil of the same 
resistance in both A and B, their ratio therefore being unity. 
Various plugs are then removed from R until with both battery 




Fig. 135. 

and galvanometer keys closed the apparatus is as nearly balanced 
as possible. At this point the sum of the unplugged resistances 
in R is as near the unknown resistance X as it is possible to get 
with the ratio of unity in B/A. 

319. Bracketing. — The plugs in R are not removed at hap- 
hazard but preferably the resistance should be arrived at by a 
system of "bracketing." For example, the first plug to be removed 
should be selected so that the resistance thrown in is certainly 
greater or less than the one to be measured. Suppose it to be less. 
The battery key K is closed and then the galvanometer key H. 
Suppose the galvanometer needle to be deflected to the left. 
Replace the plug and remove a second one so as to throw in a 
resistance certainly greater than that to be measured. Upon 
closing the keys, if the needle is now deflected to the right the 
unknown resistance lies between the two. Replace the plug and 
remove a third which will throw in a resistance as near half way 
of the interval between the first two as possible. If upon closing 
the keys the needle is deflected to the left, the third resistance is 
too small, if to the right it is too great. Proceed in this way 
keeping the unknown resistance between limits and halving the 
interval at each successive attempt. 



'242 ELEMENTS OF ELECTRICITY. 

With a little experience the bracketing can be materially 
shortened by observing the amount of swing produced in the 
needle by the trial resistances. This decreases rapidly as the 
correct resistance is approached and indicates which of two is the 
nearer. 

320. Order of Closing Keys. — The order in which the battery 
and galvanometer keys are closed is not a matter of indifference. 
It is essential that the battery key be closed first. For consider 
Fig. 135. The coils in R are wound so as to avoid self-induction 
but this object may not be completely attained and with a number 
of coils unplugged the inductance may not be negligible. Again, 
if the resistance X be that of a coil, especially if it be wrapped 
around an iron core, its self-induction will be large. Finally, if X 
be a cable it may have considerable capacity as a condenser. In 
any of these cases, when the battery key K is closed the current 
will not rise at once to its full strength in the branch affected. 
Suppose the bridge to be balanced accurately and the galvanom- 
eter key closed first; when K is closed the current in one branch 
or the other not rising at once to its full strength, M and N will 
be momentarily at different potentials and there will be an in- 
stantaneous rush of current through G causing a deflection of the 
needle and incorrectly indicating a lack of balance. On the other 
hand, if K be closed first there will still be this retardation but its 
effect will disappear in a fraction of a second, M and N will reach 
the same potential and when H is closed there will be no deflection 
of the galvanometer needle. 

There may be used a^special key which by making successive 
contacts as it is pressed down will insure the proper sequence of 
closing. 

To avoid violent swings of the needle, the galvanometer key at 
first should be given a mere tap. 

321. Proper Ratio to Use. — The first determination gives the 
resistance of X to the nearest unit or ohm. If it be desired to 
measure it to the first, second, or third place of decimals, the plugs 
in A and B must be so adjusted that the ratio B/A is .1, .01, or 
.001 and the corresponding decimal places are pointed off in the 
final reading of R. If the resistance to be measured be large, the 
ratio B/A must be 10, or 100, or 1000. 

It will be noted that some of the ratios can be obtained by several 



VOLTAIC ELECTRICITY. 



243 



different combinations, thus \%, \%%, \%%%, all give the ratio unity. 
It can be shown that other things being equal, the greatest sensi- 
bility is obtained when the resistances in the four arms of the 
bridge are as nearly equal as possible. For example, if the resist- 
ance to be measured is about 100 ohms and this is to be measured 
to the nearest unit, the ratio should be {%%, or if to the nearest 
tenth then T ^V 

The instrumental sensibility depends directly upon the sensi- 
tiveness of the galvanometer, or its ability to indicate very minute 
currents when the bridge is nearly balanced. 

322. Bridge with Reversible Ratios. — There is sometimes used, 
instead of the bridge described above, a variation by which a coil 
is saved in each of the arms A and B, making six instead of eight, 
and yet the same ratios are preserved. 




Fig. 136. 

Its arrangement is shown in (2) in Fig. 136 and is as if the arms 
A and B of (1) had been separated at S and each rotated outward 
from the center. These outer ends (2) are then connected by a 
heavy wire with S which must now be regarded as the junction 
of A and B and, according to Par. 317, is the point at which the 
battery current enters. The inner ends of A and B are connected 
to the R and the X arms by movable plugs. With the plugs in 
the positions shown by the small circles in (2), A is connected to 
R and B to X. If these plugs be shifted to the positions marked 
by the crosses, A becomes connected to X and B to R, in other 
words (see Par. 317), A and B interchange. 



244 ELEMENTS OF ELECTRICITY. 

The A arm contains the coils 1, 10, 100, the B arm 10, 100, 
1000. The smallest B/A ratio obtainable with the plugs in the 
first position is T V°o or .1. If it be desired to use a smaller one, shift 
the two plugs, A becomes B and B becomes A, and the ratios 
T ^o and T oV o become available. 

323. The Dial Bridge. — In the bridges described above, resist- 
ances are thrown in the rheostat by removing plugs. There are 
other forms, such as the dial bridge and the decade bridge, in 
which resistances are introduced by inserting plugs. The connec- 
tions of a dial bridge are shown diagrammatically in Fig. 137. 

(Doooaboooo^ 




The A and B arms are like those of the ordinary bridge but the 
rheostat is composed of dials, usually four, which are marked 
units, tens, hundreds, and thousands, respectively. Each dial 
consists of a heavy center piece of brass surrounded by ten key- 
stone shaped pieces, these being numbered 0, 1, 2, etc., to 9. 
Between the successive keystone pieces, except numbers 9 and 0, 
are resistance coils, those at each dial being all of the same 
resistance. Thus, at the unit dial each coil has a resistance of one 
ohm; at the ten dial each has a resistance of ten ohms, and so on. 
The current entering by A goes to the center of the first dial, then 
through the plug to the corresponding keystone piece, thence 
through the coils in series to the keystone and thence to the 
second dial, etc. The diagram represents a resistance plugged in 
of 5135 ohms. 

This form is more expensive than the first but has a number of 
advantages, among them, the smaller number of plugs to be 
handled and consequent smaller number of contacts (four as com- 
pared to fifteen or more) and the much less danger of error in 
reading off resistances. 



VOLTAIC ELECTRICITY. 



245 



324. Resistances that may be Measured by Bridge. — The 

bridge is not suited to the measurement of very high or of very low 
resistances. Theory requires that with the plugs inserted the 
resistances in the arms should be zero while, as a matter of fact, 
they have a resistance which may affect the fourth place of deci- 
mals. The resistance in the contacts of the plugs themselves may 
affect the third place. Therefore, in measuring very small resist- 
ances these neglected resistances may cause a considerable error, 
and in the case of a very large resistance any error in the balance 
is multiplied a hundred or a thousandfold by applying the ratio 
B/A. In general, the measurements should lie between .01 and 
100,000 ohms. 

325. The Slide Wire Bridge. — A simplified form of bridge, used 
especially in the measurement of low resistances, is the so-called 
slide wire bridge. This consists (Fig. 138) of a wire WW of uniform 




Fig. 138 



cross-section stretched between heavy copper terminals and above 
a graduated scale. Since this scale is usually a meter subdivided 
into millimeters, the instrument is often called a "meter bridge/' 
Connections are made as shown in the figure, R being a standard 
resistance coil (Par. 311) whose resistance is preferably as near as 
possible to that of X, the resistance to be measured. The terminal 
P of the galvanometer is slid backwards and forwards along the 
wire WW until balance is attained, at which point, if A and B 
be the resistances of the corresponding portions of the wire, we 
have, as in any other bridge, X = BR/A. Since the wire is of 
uniform cross-section, the resistance of the portions is directly 
proportional to their lengths, hence in the above expression the 
lengths of A and B, which may be read directly from the printed 
scale, can be and are used instead of the actual resistances, which 
last need not be known at all. 



246 



ELEMENTS OF ELECTRICITY. 



326. Measurement of High Resistance. — The principle of the 
measurement of high resistance is simple. We measure accurately 
the current driven through the resistance by a known E. M. F., 
whence, by Ohm's law, the resistance is obtained at once. For 
example, to measure the resistance of the rubber insulation of a 
reel of submarine cable, the entire cable, except the two free ends, 
is submerged in a tank of water (Fig. 139). To one of the ends of 




Fig. 139. 



the cable core is attached a terminal of a battery. The other 
terminal is connected to G, a very delicate current-measuring 
instrument (a reflecting galvanometer, Par. 378), and the circuit 
is completed by a wire extending from G and dipping into the water 
in the tank. The E. M. F. of the battery is measured by the 
instrument V, and the resulting current by G, whence R follows 
from Ohm's law. Reflection will show that should the total 
length of the cable be n yards, the average resistance per yard is 
n times the total resistance. In actually carrying out this measure- 
ment, many refinements and precautions are observed, not 
necessary to mention here. 

327. Measurement of Resistance of Electrolytes. — The re- 
sistance of an electrolyte can not be measured by the means 
described above. We have seen (Par. 215) that the passage of a 
current through an electrolyte produces chemical decomposition; 
the current used in balancing a bridge would therefore bring about 
this electrolysis. If gas be released at either anode or cathode, the 
resistance which we are trying to measure would be very greatly 
increased. Also the products of electrolysis will still set up a back 
E.M.F. which by cutting down the current through the electrolyte 
would lessen the drop in the corresponding branch and render value- 
less observations based on movements of the galvanometer needle. 



VOLTAIC ELECTRICITY. 247 

We may, however, make these measurements by employing a 
rapidly alternating current, that is, a current which many times 
a second reverses its direction of flow. In this case, a galvanometer 
can not be used to indicate a balance but in its stead a telephone 
receiver is employed, taking the place of G in Fig. 138. So long as 
an alternating current flows through the receiver a buzzing sound 
is produced, but when the bridge is balanced the sound dies out. 
Explanation of these facts will be given later. 

328. Measurement of Internal Resistance of Cells. — In meas- 
uring the internal resistance of a cell the same difficulties are 
encountered as in the case of electrolytes and in addition the cur- 
rent produced by the cell itself prevents the use of the bridge. 
There are, however, several methods by which this internal 
resistance may be measured. The simplest is by using the instru- 
ments for measuring E. M. F. and current, which instruments 
will be described in Chapter 34. We first measure the E. M. F. 
of the cell when no current is flowing. We then cause a moderate 
current to flow from the cell, measure this current and the external 
or useful volts (Par. 305). The difference between the E. M. F. 
of the cell and the useful volts is the lost volts or Ir, and knowing 
I we determine r. 



248 ELEMENTS OF ELECTRICITY. 



CHAPTER 27. 

THE POTENTIOMETER. 

329. Measurement of Electro-Motive Force of Cells. — The 

simplest and usual way of measuring the electro-motive force of 
a cell is by means of a voltmeter, an instrument described in Chap- 
ter 34. It will be shown, however, that in order to obtain a read- 
ing from the voltmeter, there must be a flow of current through 
the instrument. It is true that this current is so small that for 
all ordinary cases it is entirely negligible, but if there be a current 
there will also be lost volts (Par. 305) and since a voltmeter reads 
only the useful volts, its indications are always some slight 
amount less than the true E. M. F. Therefore, to obtain strictly 
accurate results, the E. M. F. of a cell should be measured when 
no current is flowing. This may be done with an electrometer, 
as explained in Chapter 11, but preferably by a potentiometer, an 
instrument which we shall now describe. 

330. Preliminary Arrangement of a Potentiometer. — Let us 
suppose that we start with one or two cells giving us a constant 



w — ^ 

^7 



iiimiiiimmimimiimiimiiiimiimmmiiiimiitiiimiii Hiiimiiiiiiiimimiim 



Fig. 140. 

E. M. F. of about two volts, seven or eight feet of rather thin wire 
of uniform cross-section, and a graduated paper scale. Provided 
the scale be graduated uniformly, the unit is immaterial, but a 
millimeter scale running up to 2000 is very convenient. We will 
tack the paper scale upon a board AB (Fig. 140), and stretch the 
wire above it. To the end A of the wire we connect the negative 
terminal of our cell C; the other terminal makes sliding contact 
at P. 



VOLTAIC ELECTRICITY. 249 

If the E. M. F. of the cell be two volts, the difference of potential 
between P and A before P is touched to the wire will be two volts 
and after contact is made it will still be about two volts. If it were 
exactly two volts when P is at the 2000 division on the scale, 
there would be a drop of two volts from P to A and each division 
of the scale would correspond to a drop of one-thousandth of a 
volt. If P be slid in towards A, these two volts will be spread 
over a shorter length of the wire and each division on the scale 
would correspond to a drop of more than one-thousandth of a volt. 
On the other hand, if P be slid out from A, the scale divisions can 
be made to correspond to less than one-thousandth of a volt, 
therefore, by sliding P backwards and forwards we can vary the 
drop over the scale and at one particular point this drop will be 
exactly one-thousandth of a volt per millimeter. This point is 
located as follows: 

331. Calibration of Potentiometer. — To the same end A of 
our stretched wire we connect through a galvanometer G the 
negative terminal of a standard cell S. If this be a Clark's cell 
whose E. M. F. is 1.434 volts (Par. 212), we connect its positive 
terminal to the wire at M, a point 1434 millimeters from A. If 
M be at a higher potential than 1.434 volts a current will flow 
from M to D, while if it be at a lower potential a current will flow 
from D to M. In either case this flow will be indicated by a 
deflection of the needle of the galvanometer G. If there be a flow, 
we slide the contact P backwards or forwards until a point is 
found where G indicates no current and we then know that the 
potential of M is the same as that of D, that is, 1.434 volts, and 
that consequently each division of the scale corresponds to a drop 
of one-thousandth of a volt. The contact P is left at this point, 
for unless a current flows from P to A there will be no drop of 
potential along PA. There is no difference of potential between 
two points of a conductor unless a current is flowing between 
these points. The instrument is now in adjustment so that the 
printed figures on its scale read thousandths of a volt, in other 
words, it has been calibrated. 

332. Measurement with Potentiometer. — To measure the 
E. M. F. of a cell X, its negative terminal is connected through 
the galvanometer H with A and its positive terminal is con- 
nected to a contact T which is moved back and forth along the 



250 ELEMENTS OF ELECTRICITY. 

wire until H indicates no current. Suppose this point to be 
the 925th millimeter from A, then the E. M. F. of X is .925 
volt. 

Instead of using a second galvanometer H, the negative ter- 
minal of X could have been attached to G, that is, S and X can 
use G in common. Measurements can not be made by placing 
T to the right of P. 

333. Forms of Potentiometer. — As in the case of the Wheat- 
stone bridge, the actual instrument bears no resemblance at all 
to the diagrammatic representation in Fig. 140. For example, 
for the sake of compactness the long wire is wound in a helical 
coil around an ebonite cylinder, etc., etc. There are numerous 
forms of potentiometers but the principle of all is the same, that 
is, they measure an unknown E. M. F. by balancing against it an 
equal and opposite E. M. F. which latter is known. 






VOLTAIC ELECTRICITY. 



251 



CHAPTER 28. 



GROUPING OF CELLS IN BATTERIES. 

334. Grouping of Cells. — The cells composing a battery may 
be connected up in several ways. If they are connected one after 
the other they are said to be in series. If all of the positive poles 
are connected to one common wire and all of the negative poles to 
another, they are said to be in parallel. If they are divided into 
groups, the cells in each group being connected in series and these 
separate groups being then connected in parallel, the battery is 
said to be grouped in multiple, or better, so many in parallel and 
so many in series. For example, if we have ten cells we might 
group them all in series, or all in parallel, or two abreast and five 
deep, that is, two in parallel and five in series, or finally, five 
abreast and two deep, that is, five in parallel and two in series. 
Each of these arrangements is quite proper under certain condi- 
tions but it will be shown in the following paragraphs that it is 
not a matter of indifference which shall be employed. 

335. Cells in Series. — In Par. 192 we saw that in a voltaic cell 
the copper or positive pole is at a higher potential than the zinc 
or negative pole. Suppose that we have a number of simple cells, 
each of an E. M. F. of one volt, and that we should arrange them 




in series, the copper plate of each, as shown in Fig. 141, being 
connected to the zinc plate of the adjoining one. The copper 
plate of A and the zinc plate of B being connected are at a com- 



252 



ELEMENTS OF ELECTRICITY. 



mon potential, therefore the zinc plate of B is one volt higher than 
that of A. The copper plate of B being one volt higher than its 
zinc plate is consequently two volts higher than the zinc plate of A. 
Similarly, the copper plate of C is three volts higher than the zinc 
plate of A, and in general the total E. M. F. of a number of similar 
cells connected in series is equal to the E. M. F. of one cell multi- 
plied by the number in series. This principle applies even though 
the circuit includes cells of different kinds, electrical machines, 
etc., and the most general statement is that in any electric circuit 
containing several sources of E. M. F. in series the total E. M. F. 
is the sum of the separate E. M. F.s. 

336. Cells in Parallel. — Fig. 142 represents three cells in 
parallel. The three positive poles being brought together at a 
common point A are all at the same potential, that is, one volt 
higher than the three negative poles which are brought together 




at B. This combination therefore has no greater E. M. F. than 
has a single cell and it is in fact, as we have already seen (Par. 
294), equivalent to a single cell whose copper and zinc plates are 
three times as large as those of the original cells. 

337. Comparison of Series and Parallel Groupings. — We may 

by a concrete example best illustrate the different effect of the 
two kinds of groupings. Suppose that we have a number of cells, 
each of an E. M. F. of 2 volts and an internal resistance of .25 ohm. 
From a single cell in a circuit of negligible external resistance the 
current obtainable is 

7= 4"r = 0TT5 = 8amperes 






VOLTAIC ELECTRICITY. 253 

With two in series, the E. M. F. is twice as great (Par. 335;, 
but also the resistance is twice as great (Par. 286), therefore the 
current is the same, and so on for any number, that is, with a cir- 
cuit of negligible external resistance the effect of grouping cells 
in series is to increase the voltage but not the current. Should, 
however, the external resistance be great, a different state of 
affairs results. For example, let R = 100 ohms (the resistance of 
about 6 miles of iron telegraph wire), then for one cell 



and for two cells 



I = 



100 + .25 



100 + .50 



The difference in these denominators being negligible, we see that 
in this second case we have doubled the current. 

If, starting again with negligible external resistance, we arrange 
two of these cells in parallel, the E. M. F. is no greater than for 
one cell (Par. 336) but the resistances of the two cells being in 
parallel, the total resistance is only one-half that of one cell (Par. 
293), hence the current is doubled. For three cells it is trebled, 
and so on, that is, with negligible external resistance, the effect 
of grouping cells in parallel is to increase the current but not the 
voltage. 

With a large external resistance, the grouping of cells in parallel, 
since it does not increase the E. M. F. nor change the total resist- 
ance to any significant extent, does not alter the current. 

We may sum up by saying that with a large external resistance 
we increase the current by grouping the cells in series; with a 
small external resistance, we increase it by grouping them in 
parallel. 

338. Analogy Between Voltaic Cells and Pumps. — Difference 
of potential has been compared to difference of water level (Par. 
70). Since a difference of potential is produced in a cell, we may 
continue the comparison by drawing an analogy between a cell 
and a pump. In Fig. 143 the pumps A, B and C are analogous to 
three cells in parallel; they lift the water no higher than a single 
pump but they lift thrice the quantity. The pumps C, D and E 



254 



ELEMENTS OF ELECTRICITY. 



are analogous to cells in series; they lift no more water than a 
single pump but they raise it three times as high. 



^ (f^/m 





339. Parallel -Series Grouping. — Suppose we have N cells, 
each of an E. M. F. of e volts and an internal resistance of r ohms, 
and suppose that they are arranged (Fig. 144) s in series and p in 



i ii ii ii 



^-•llllllllllllll^ 


\|i|i|i|i|i|i|iK 


R 



Fig. 144. 

parallel in a circuit of external resistance R. The resulting E. M. 
F. is equal to the E. M. F. of one cell multiplied by the number in 
series (Par. 335) or se. The resistance of one of the series is rs, 
but since there are p rows in parallel, the total internal resistance 
. rs 



is 



V 
The current produced by this arrangement is 



I = 



R + r 



V 



340. Maximum Current. — The question may arise, given N 
cells, how should they be grouped to obtain the maximum current? 



VOLTAIC ELECTRICITY. 255 

The expression for the current is given in the preceding paragraph 
and, since N = sp, can be written 

Ne 



I = 



NR , 

h rs 

s 



If this be differentiated and the first differential coefficient be 
placed equal to zero, the resulting values of s will correspond to 
maximum or minimum values of I. This differentiation is tedi- 
ous. However, since Ne is a positive constant, / will be a maxi- 

NR 

mum when + rs, the denominator of the expression, is a 

S 

minimum. 

NR 
Place x = - — + rs = NRs~ l + rs 



Differentiating 



dx A7D 2 i NR 

-jz = — NRs— 2 -\-r—r =- 



ds s s 

Placing this equal to zero, we have 

2 NR u JNR 

s 2 = , whence s = ± y 

r V r 

which is the value 
sought. This will in general only approximate to the desired 
arrangement since the mathematical supposition is that s and p 
are continuous variables, while actually they are both discon- 
tinuous or positive whole numbers. For example, if N be 10, 
the only possible values of s are 1, 2, 5 and 10, yet the actual 
solution will generally produce some mixed number. In such a 
case we should make the calculation of the current from the two 
groupings which come nearest to the one indicated by the solution 
and select accordingly. 

If in the above equation of condition for maximum current 

. NR 



s* = 



we substitute for N its value 



sp, we get S pR 

s 2 = — — 



whence R= r- 



256 ELEMENTS OF ELECTRICITY. 

But (Par. 339) R is the external resistance and r— is the 

V 
internal resistance, whence we arrive at the important conclusion 
that the current is a maximum when the battery is so grouped that 
the internal and the external resistances are equal. 

We saw (Par. 305) that the useful volts of a cell or battery are 
given by IR, the lost volts by Ir. Since in the case of maximum 
current R =r, the lost volts amount to one-half of the total E. M. F. 

341. In Multiple Arrangements Equal E. M. F. is Required 
of Groups in Series. — In a parallel-series arrangement the series 
groups must all have the same E. M. F. This requires that where 
the cells are all of one kind there should be the same number in 
each series group. The arrangement shown in Fig. 145 is not 




Fig. 145. 

permissible. The battery should be quiescent when the key K 
is open but the three cells now constitute a closed circuit in which 
the E. M. F. of the two upper cells acting in a clockwise direction 
is not counterbalanced by the opposing E. M. F. of the single 
cell. If the E. M. F. of each cell be e and its resistance r, there 
will flow through the single cell a reverse current whose strength 

is / = s— . The elements of the two upper cells will therefore 
3r 

consume away and the zinc plate of the single cell will have copper 
deposited upon it which will cause local action. With K closed, 
the loss is not so great and it will diminish as the external resist- 
ance decreases, but even in this case the elements of the single 
cell will consume away much more rapidly than those of the two 
in series. 

342. Diagrams of Parallel-Series Grouping. — A parallel-series 
grouping represented as in Fig. 144 doubtless aids the beginner, 
but in actual practice cells are seldom arranged in this geometrical 
order. Especially is this the case with storage batteries in which 



VOLTAIC ELECTRICITY. 



257 



the cells are very heavy and are placed in rows on shelves or 
benches. Reflection will show that after all it is not necessary to 
move the cells themselves but rather to shift the connecting 
wires. Thus in Fig. 146 eight cells are represented in four different 



t 



i i 



i i 



k fi| 



\ ii i 



/i|i|i[i|i|ifi[iP J 



i i 



J I 



rl I 



Fig. 146. 

groupings, the cells themselves not being disturbed. In A they 
are all in series, in B all in parallel, in C four in series and two in 
parallel, and in D two in series and four in parallel. 

343. Cost of Power from Primary Cells. — For the small and 
irregular currents required in telegraphy and in operating tele- 
phones, call bells, annunciators, alarms, etc., a battery of primary 
cells is the most suitable and economical source of electrical 
energy, but where the current is required to furnish appreciable 
mechanical power through suitable machines, the cost is pro- 
hibitive. The chemicals consumed in the cell correspond to the 
fuel consumed in the boiler of a steam engine, and while one 
pound of carbon burned in air evolves enough heat to raise 8080 
pounds of water 1° C, in round numbers four pounds of zinc must 
combine with six pounds of sulphuric acid to produce the same 
amount of heat. With modern machines electrical energy may 
be produced as cheaply as one cent per horse-power per hour but 
the same energy supplied from primary cells costs from 30 to 
50 times as much. Where many telephones or telegraph lines 
are operated from a central station it is now the practice to use 
storage batteries instead of the batteries of Daniell or gravity 
cells formerly employed. 



ELECTRO-MAGNETICS. 259 



PART IV. 
ELECTRO-MAGNETICS. 



CHAPTER 29. 



MAGNETIC FIELD ABOUT A WIRE CARRYING 
A CURRENT. 

344. Oerstedt's Discovery. — In 1819, in the course of a lecture 
on electricity, Oerstedt, Professor of Physics at Copenhagen, 
observed that when a wire carrying a current was brought near a 
magnetic needle a deflection of the needle was produced. He 
recognized at once the importance of this discovery as demon- 
strating what up to that time had been merely a conjecture, that 
is, that there existed some connection between electricity and 
magnetism. He set to work immediately to investigate the matter 
and soon discovered not only that an electric current produced a 
deflection of a magnetic needle near it but that the direction of 
this deflection depended both upon the direction in which the 
current was flowing and upon the position of the conductor with 
reference to the needle. His results were announced in 1820. 
The news reached the French electrician Ampere on September 11 
and was received by him with eagerness. Within one week there- 
after he had repeated Oerstedt's experiments and had added to 
the latter's discoveries; had confirmed by specially devised experi- 
ments and had presented in a paper to the Academy a complete 
theory of the new science of electro-dynamics (Par. 360) . 

345. Right Hand Rule for Deflection of Needle.— It is helpful 
to the electrician, whether he be an advanced student or only a 
beginner, to have some easy rule for determining, or some mechan- 
ical way of remembering, in which direction certain phenomena 
take place. Thus Ampere gave the rule of the "swimming man" 
by which, the relative positions of the conductor and of the needle 
and the direction of the current being given, the direction in 



260 ELEMENTS OF ELECTRICITY. 

which the north end of the needle would move could be predicted. 
Other rules have been given by subsequent writers. Of these, 
the following is thought to be the most useful, both because of 
its simplicity, it being a true "rule of thumb," and because, as will 
be shown later, of its applicability to a number of varied con- 
ditions. It should be committed to memory. 

Place the palm of the right hand upon the wire, the extended 
fingers pointing in the direction of the flow of the current, the palm 
turned towards the needle; the extended thumb will indicate the 
direction in which the north pole of the needle will move. 

Fig. 147 represents the application of this rule. The current 
flowing in the wire in the direction indicated by the arrow will 




Fig. 147. 

cause the north pole of the needle to move out in the direction in 
which the thumb is pointing. If the wire be held below the 
needle, the hand must be held back down, in which case the 
thumb will point away from the observer. 

346. Magnetic Field About a Wire Carrying a Current. — In 

Pars. 143 and 144 it was shown that a needle in a magnetic field 
tends to turn so as to place its longer axis and its own lines of 
force parallel to the lines of force of the field. The needle in 
Oerstedt's experiment turns for the same reason, that is, the cur- 
rent flowing through the wire establishes about this wire a mag- 
netic field with which the needle tends to coincide in direction. 
The above rule, therefore, is really one for determining the posi- 
tive direction of that portion of the field on the opposite side of 
the wire from the palm of the hand. If the wire be wrapped in a 
coil, this rule determines the positive direction of the field within 
the coiL 



ELECTRO-MAGNETICS. 



261 



This field may be studied in a similar manner to the other 
magnetic fields already described. If a vertical wire, a portion 
of an electric circuit, be passed through a hole in the center of a 
horizontal sheet of cardboard 
or of glass which has been 
sprinkled with iron filings (Fig. 
148) and if the circuit be then 
closed and the horizontal sheet 
be tapped while the current is 
flowing, the filings will be seen 
to gather and form in more or 
less distinct circles around the 
wire as a center. The lines of 
force of the field are circles, 
and it was shown first by 
Ampere that these circles lie 
in planes perpendicular to the 
wire. In Oerstedt's experiment as described in Par. 344, the needle 
can never place itself at right angles to the wire, for the controlling 
force, the horizontal component of the earth's magnetism, is 
always effective. However, if a perfectly balanced needle be 
mounted so that its axis of rotation is parallel to the earth's field, 
then this field has no influence upon its rotation and if Oerstedt's 
experiment be now performed, the needle will always set itself 
at right angles to the wire. 




Fig. 148. 




347. Direction of Field. — The experiment with the iron filings 
shows the lines of force of the field to be circles but does not 
indicate their direction. This latter may be determined as follows. 



262 ELEMENTS OF ELECTRICITY. 

Using the same horizontal sheet and vertical wire as in the pre- 
ceding experiment, distribute at equal distances apart on the 
circumference of a circle whose center lies on the wire a number 
of small compasses, A, B, C, D (Fig. 149). Before the circuit is 
closed, these all point in the same direction. Let us assume that 
this is the direction indicated by the needle A. Suppose now the 
circuit to be closed and the current to flow down the wire. The 
needle at A will not change its position, C will be entirely reversed, 
B will point to the right and D to the left, that is, if we look at 
the needles from above, they point around the circle in the direc- 
tion of the motion of the hands of a clock. Had the current 
flowed up, the needles would all have pointed in a counter-clock- 
wise direction around the circle. 

348. Clock Rule for Direction of Field. — The foregoing experi- 
ment suggests another simple rule for determining the direction 
of the field about a wire carrying a current. 

Suppose the eye placed so as to look along the wire in the direction 
in which the current is flowing; the positive direction of the field 
about the wire is the same as the direction of motion of the hands 
of a clock. 

Of course, if the current is flowing towards the eye, the field is 
counter-clockwise. This rule should not supplant the right hand 
rule given in Par. 345. Either one could be used to the exclusion 
of the other but it is better to have both at command. 

349. Wire Carrying a Current is not Itself a Magnet. — Although 
surrounded by a magnetic field, a wire carrying a current is not 
itself a magnet. If a clean copper wire through which a current 
is flowing be dipped into iron filings and then lifted, the filings 
will cluster around the wire but will drop off when the current is 
broken. At first sight this seems to indicate that the wire has 
become magnetized but it can be shown that such is not the case. 
When the wire is thrust into the filings they become magnetized, 
since magnetic bodies placed in a magnetic field become magnets 
(Par. 120), and if they surround the wire, or if any of them adhere 
to it through stickiness, they cling together like the links of a 
chain and really adhere to each other instead of to the wire. If 
an elongated filing be placed at right angles to the wire and with 
its ends lying upon one of the circular lines of force surrounding 
the wire, one of these ends will be urged in one direction around 



ELECTRO-MAGNETICS. 



263 



the circle, the other end in the opposite direction; the result is 
that the filing will move broadside towards the wire. There is, 
however, no radial component between a wire carrying a current 
and a magnetic pole in its field. In this respect the field about a 
conductor is unique. While all other forces exerted between 
bodies act along the line joining the bodies, the force upon a pole 
in a field about a wire acts at right angles to the line joining the 
wire and the pole. 

350. Rotation of a Magnetic Pole by a Current. — In Par. 135 
the positive direction of a magnetic field was defined as that direc- 
tion in which a free north pole would move. Such a pole released 
near the north end of a magnet would move off along a line of 
force, curving around until it came to rest against the south face. 
The statement was made (Par. 142) that a magnetic line of force 
is a closed curve, but the moving 
pole can not travel around a com- 
plete orbit for its progress is arrested 
by the material substance of the 
magnet. In the field about a wire 
carrying a current the case is dif- 
ferent. Here the lines of force are 
circles, return upon themselves and 
do not necessarily pass through any 
solid body. A pole released in such a 
field should therefore rotate as long 
as the field is maintained. Although 
we can not obtain a free pole, we 
can approximate to the theoretical 
condition by arranging a circuit so 
that only one pole of the magnet 
lies in the field and we can thus 
produce mechanical rotation. 

Fig. 150 represents diagram- 
matically such an arrangement. NS 
is a magnet bent in the center at an angle and placed upon the 
pivot P about which it is free to rotate. B is a little cup of 
mercury into which dips the conductor A B, thereby securing 
movable electric contact with a minimum of friction. CD is an 
annular cup of mercury surrounding but not touching the magnet. 
From B a wire BD is carried over and bent down so as just to 




Fig. 150. 



264 



ELEMENTS OF ELECTRICITY. 



touch the surface of the mercury at D and to sweep along this 
surface as the magnet rotates. DE is a conductor leading away 
from the annular cup. If the current enters at A, it goes to B, 
thence to D and out by E. It therefore passes by the pole AT" but 
not by the pole S. According to the rule given in the preceding 
paragraph, the field about A B, viewed from A, is clockwise. The 
pole N will therefore spin around in the direction shown by the 
dotted line. If the current be reversed the direction of rotation 
is also reversed; so also if the magnet be inverted, the direction 
of rotation is reversed. 

351. Rotation of a Current by a Magnetic Pole. — The reaction 
between the pole and the field being mutual, it follows that if 

the pole be fixed and the conductor be free 
to move, the latter may be made to rotate 
about the former. This may be shown by 
the apparatus represented in Fig. 151. NS 
is a magnet run through a cork which is 
inserted in the lower end of a short and 
broad glass tube. The annular space around 
the projecting pole N is filled with mer- 
cury. A current is led down by the wire A, 
through the flexible joint and B into the 
mercury cup and out by C. While the 
current flows B is surrounded by lines of 
force which viewed from A are clockwise. 
If B were stationary and N were free to 
move, N would travel around B in a clock- 
wise direction, that is, N would move out 
towards the observer. However, N being 
fixed, B moves back from the observer and 
travels around N in a clockwise direc- 
Fig. 151. tion. 

352. Left Hand Rule for Direction of Motion.— The con- 
ductor described in the preceding paragraph is in the field of 
the magnet and owes its motion to the interaction of this field 
with its own. Any conductor carrying a current and placed 
in a magnetic field will move if it be ' free to do so. It is 
useful to have a rule by which the direction of this motion 
can be foretold. The following is such a rule. Place the palm 




ELECTRO-MAGNETICS. 



265 



of the left hand upon the wire, the extended fingers pointing in 
the direction of the flow of the current (Fig. 152) and the palm 
turned to receive the lines of force of 
the field; the extended thumb will point 
in the direction of the motion of the con- 
ductor. 

353. Intensity of Field About a 
Straight Conductor. — A magnetic field 
is known when we have determined its 
direction and intensity. We have 
shown above (Par. 347) how to deter- 
mine the direction of the field about 
a conductor carrying a current. The 
intensity may be measured as ex- 
plained in Pars. 148-150. In two sim- 
ple cases (which fortunately are the 
ones most frequently encountered), it 
may be calculated. These are, first, 
when the conductor is straight, and 
second, when it is bent into the arc 
of a circle. 

In Fig. 153 let AB represent a por- 
tion of a straight wire of indefinite length carrying a current of 
strength /. (The unit in which / is measured is for the moment 
r held in abeyance; see Par. 355.) Let m 

represent a unit pole at a distance r from 
the wire. The force exerted upon m will 
measure the intensity of the field at that 
point (Par. 136). Let A represent an 
infinitely small section of the wire, its 
length being dy. Since the current is the 
same at every cross-section, the quantity 
of electricity moving in the section A is 
proportional to the length of this section, 
or is I.dy. The force which this exerts 
upon a unit pole at b is 




-b 



'■a ' 



>- m 



3 



Fig. 153. 



df = 



I.dy 



266 ELEMENTS OF ELECTRICITY. 

and that exerted at m, oblique to the section A, is 

df = ^. sin a (I) 

This expression integrated between proper limits will give the 
intensity of the field produced at m by the corresponding lengths 
of AB. 

r 



From the figure x 
also y = 



sin a 



, hence dy = r ( — cosec 2 a da) 



tan a 

Substituting these values in (I) and remembering that 
1 



cosec a 



sin a 



we obtain 



df = . sin a da 

r 



/.=•-. cos a + a constant. 
r 



Integrating 

Taking this between the limits a = 0° and a = 180°, we have 



/ = 



2/ 



or the field at any point 
about an indefinitely long straight wire is directly proportional to 
the current and inversely proportional to the simple distance from 
the wire. 

354. Field on the Axis of a Circular Coil. — The field produced 
at a point on the axis of a circular coil may be determined as 




> : D 



Fig. 154. 



follows: With a current of strength I flowing as indicated by the 
arrow (Fig. 154), the infinitely small portion of the coil at A exerts 



ELECTRO-MAGNETICS. 267 

upon a unit north pole at P a force in the direction PF which is 
-^-, d£ being the length of A. This may be divided into two 

JO 

components, one PD = — '— • sin 0, and the other PE. The 

JL 

diametrically opposite element of the coil at B likewise exerts a 

force upon P which may be divided into two components, one in 

the direction PD, the other opposite and equal to PE and hence 

counterbalancing it. Every element of the coil therefore exerts 

in the direction PD a force upon P equal to 

Ldl . 
— — . sin 6 

x 2 

The sum of these elementary forces is 
f = -tfT • sm * 

Substituting for sin its value r/x 

or, the field at any point 
on the axis of a circular coil varies directly with the current and 
inversely as the cube of the slant distance. 

If the point P be moved to the center of the coil, x becomes 
equal to r and the above expression becomes 

, 7.2t 



Should the coil consist of n turns, the field produced is n times 
as strong as that produced by one turn, therefore, the above 
expressions for the field must be multiplied by n. 

355. Absolute Unit of Current. — An important consequence 
follows from the foregoing. Since the field at the center of a 
circular coil varies directly with the current, the measure of the 
field may be used as a measure of the current. This may be 
shown as follows. 

Since, as has just been seen, we obtain the intensity of the 
field at the center of the coil by adding up the effects produced 
by each infinitesimal section of the coil, the field produced by a 



268 ELEMENTS OF ELECTRICITY. 

portion of the coil must be directly proportional to the length of 
this portion, or, if this length be I 

J 7.2 
If in this we make r and I each one centimeter, we have 

/=/ 

Since / varies with I, there must be a particular value of / 
which will make / one dyne. At this instant J is unity, whence 
we derive at once the definition of the absolute unit of current as 
that current, which flowing through one centimeter of a conductor 
bent into the arc of a circle whose radius is one centimeter, exerts a 
force of one dyne upon a unit pole placed at the center of the circle. 

If in Fig. 155 the length of the 
conductor from a to b be one 
centimeter and if it be bent into 
the arc of a circle of one centi- 
meter radius, the current which 
flowing through this conductor 
exerts a force of one dyne upon 
the unit pole at m, has a strength 
of one absolute unit. 
The absolute unit of current, as will be explained later (Chap. 
39), is ten times as great as the practical unit, the ampere, or, 
one absolute unit equals ten amperes. Therefore, in applying the 
expressions in Pars. 353 and 354, if / be given in amperes, it must 
be reduced to absolute units or divided by ten in order that / 
should be in dynes. For actual measurement of current, see 
Par. 374. 

356. Force Exerted by a Magnetic Field upon a Conductor 
Carrying a Current. — The force exerted upon a unit pole at m by 
the field of ab (Fig. 155) is shown to be 

U 

J r 2 

If the strength of the pole be m instead of unity, the force is 

- m.I.l 

J ~ ~2 




ELECTRO-MAGNETICS. 



269 



If the current flows as shown in the figure, and if m be a north 
pole, this force acts upward. An equal downward force acts 

YYl 

upon ah. In the above expression -j is the field along ah due to 
the pole m (Par. 136) and is uniform. Calling this H, we have 

f= I.H.I 

or, the force exerted by a 
magnetic field upon a conductor carrying a current and at right 
angles to the field is proportional to the current, to the intensity 
of the field and to the length of the conductor. This force is at 
right angles to the field and to the conductor and, as explained 
in Par. 355, is expressed in dynes when I is in absolute units. 

Fig. 156 represents a cross-section of such a conductor lying 
in a field NS. If the current is flowing away from the observer, 




Fig. 156. 

the lines of force about the wire are clockwise, therefore, on the 
upper side of the wire they coincide in direction with those of the 
field but on the lower side they are opposite in direction. The 
field is therefore distorted as shown, the lines thickening up above 
the wire and thinning out below. Since lines of force have a ten- 
sion in the direction of their length, or a tendency to shorten, the 
result is that the wire is urged downward. Application of the left 
hand rule (Par. 352) indicates this downward motion. 

357. Work Done in Moving Across a Magnetic Field a Con- 
ductor Carrying a Current. — From the preceding paragraph, the 
force exerted upon a conductor carrying a current and lying at 
right angles to the field is I.H.I dynes. 



270 ELEMENTS OF ELECTRICITY. 

If the conductor be moved at right angles to the field and to its 
own length, it will move either against this force or with it. In 
the first case, work must be done upon the conductor; in the second 
case, work is done by the conductor. In either case, if the dis- 
tance moved be x centimeters the work, being force X path, is 

W = 1 . H l.x ergs 

But l.x is the area in square centimeters swept over by the con- 
ductor in its movement, H is the number of lines of force per square 
centimeter (Par. 145), therefore H.l.x is the total number of lines 
of force cut by the moving conductor. Placing this equal to N we 

have 

W = I. N ergs 

or the work done in mov- 
ing across a magnetic field a conductor carrying a current of I 
absolute units is equal to the product of the current into the num- 
ber of lines of force cut. 

358. Work Done in Moving Across a Magnetic Field a Coil 
Carrying a Current. — This is merely a particular case of the fore- 
going but furnishes conceptions which facilitate the application 
of the principle in certain deductions which we shall make later on. 
Suppose the moving conductor to be in the form of a closed coil 
and, for the sake of simplicity, suppose this to be rectangular and 
to be moved so that while two sides cross the field at right angles 
to the lines of force the other two sides move lengthwise through 
the field. Since these latter cut no lines of force they perform no 
work. If the field be uniform each of the other two sides performs 
an equal amount of work, but the current in them flows in opposite 
directions so that in one IN is positive while in the other it is 
negative. The net result is zero, or, no matter how it may be 
moved, if in its successive positions in a uniform field a coil 
remains parallel to its original position, no work is done. 

If, however, the field be not uniform, the work done by one of 
these sides will be I N ergs, that by the other — IN' ergs, and the 
total work is I (N — N') ergs, or the work done in moving a coil 
in a magnetic field is equal to the product of the current in the coil 
into the change in the number of lines of force embraced by the 
coil. This is general, that is, it is true whatever the shape of the 
coil and whether its motion be one of translation or of rotation. 
It also follows that the same amount of energy is expended if 



ELECTRO-MAGNETICS. 271 

the coil be kept motionless and the field embraced be moved or 
varied. 

If two separate and similar coils be moved in succession across 
the field, the work done by each is, from the foregoing, / N ergs, 
in which N is the change in the number of lines of force embraced 
by the coil, the total work being 2 IN ergs. If they be moved 
simultaneously the work will be the same. Finally, they need 
not be separate coils but may be two turns of the same coil 
and still the work will be 21 N ergs. In general, therefore, if the 
field within a coil of n turns carrying a current / be increased 
or decreased by N lines of force, the work done will be nl N 
ergs. 

359. Energy Expended upon an Electro- Magnetic Field. — The 

conclusions in the preceding paragraph are irrespective of the 
origin of the field. It may therefore be produced in any way, even 
by the current itself. When a current is sent around a coil, N 
lines of force are produced in the coil. By a similar method to 
that followed in Par. 96, or by an application of the integral cal- 
culus, it may be shown that if the current starts at zero and in- 
creases to a value /, the energy expended in establishing the field 
is ^ IN ergs over and above that spent in the mere heating of the 
conductor. This energy is absorbed in the field and restored when 
the circuit is broken. This fact explains why the current never 
rises instantly to its full strength when the circuit is closed and 
also why the current always lingers after the circuit is broken, 
revealing itself as a spark. This subject will be referred to again 
when the discussion of induction is reached. 

360. Electro-Dynamics. — In Par. 356 it was shown that a con- 
ductor carrying a current and placed in a magnetic field is acted 
upon by a force at right angles to the field and to the conductor. 
Since conductors carrying currents are surrounded by magnetic 
fields (Par. 346), it follows that if two such conductors be placed 
near together, each will lie in the magnetic field of the other and 
each will be subjected to a force. Ampere, who made this dis- 
covery in 1820, applied the term electro-dynamics to that branch 
of electricity which treats of the forces exerted between currents, 
and formulated the laws given in the following paragraphs. 

361. Force Exerted Between Conductors Carrying Currents. — 

Two parallel conductors attract one another if the currents in them 



272 



ELEMENTS OF ELECTRICITY. 



flow in the same direction but repel each other if the currents flow 
in opposite directions. 

A and B, Fig. 157, are two such conductors. Considering B as 
lying in the field about A, application of the left hand rule (Par. 
352) will show that B is urged at right angles to its length and 



B 




Fig. 157. 

towards A. Similarly, A is urged towards B. Had the currents 
flowed in opposite directions the wires would have repelled each 
other. 

It may be shown by Laplace's law (Par. 353) that if the two 
wires be not parallel, the electro-magnetic effect of either current 
can be resolved into two components, one parallel to the remain- 
ing current, the other perpendicular to it and contributing noth- 
ing to the forces between the two wires. In the most general 
case, therefore, if two conductors cross, those portions in which 
both currents flow either towards or from the point of crossing 
attract each other while those portions in which one current flows 
towards and the other from the point of crossing repel each 
other. 

It is not necessary that the two conductors be parts of different 
circuits. The same law applies to portions of a single circuit. If, 
for example, a current be passed through a helical coil, the adjacent 
turns attract each other and the coil tends to shorten. 



ELECTRO-MAGNETICS. 273 

362. Intensity of Force Between Parallel Conductors Carrying 
Currents. — If the wire A, Fig. 157, be of indefinite length and if 
there be flowing in it a current of strength I', the intensity of the 
field produced by it at any point along B is (Par. 353) 

r 
r being the distance between 
the two wires. But we have seen (Par. 356) that the force exerted 
by a field H upon a wire of length I carrying a current of strength 
I is /= I. H.L Substituting in this the value of H from above, we 
have 

f _ 2in 

or the force exerted upon 
the second wire B is directly proportional to the product of the 
currents in the two wires and to the length of B and inversely 
proportional to the simple distance between the wires. 



274 ELEMENTS OF ELECTRICITY. 



CHAPTER 30. 

GALVANOSCOPES AND GALVANOMETERS. 

363. Galvanoscopes. — Oerstedt's discovery affords us a means 
of determining whether or not a current is flowing in a conductor, 
and if flowing, in what direction. For example, in the case of an 
electric wire crossing the ceiling of a room, it is only necessary to 
hold a magnetic needle an inch or so below the wire when, if a cur- 
rent is flowing, the needle will be deflected and the direction of 
this deflection, in conjunction with the right hand rule, will reveal 
the direction of flow of the current. Instruments designed to give 
information of this character are called galvanoscopes. 

364. Increase of Sensitiveness. — We frequently have to deal 
with currents so small that the deflection they produce in an 
ordinary needle is imperceptible. In such cases the only remedy 
is to increase the sensitiveness of the instrument. A needle when 
in use is acted upon by two forces; first, the deflecting force which 
causes it to move and, second, the controlling force which resists 
deflection. We therefore have two expedients; we may multiply 
the effect of the deflecting force or we may weaken the controlling 
force. The highest degree of sensitiveness is attained by com- 
bining these two. We shall now examine these in detail. 

365. Schweigger's Multiplier. — Suppose a needle to be placed at 
the center and to lie in the plane of a vertical coil. Application of 
the right hand rule will reveal the fact (shown already in Par. 
354), that when the circuit is closed, the top, the sides, the bottom 
of the coil, all contribute to produce a deflection of the needle in 
one and the same direction. As the palm of the right hand is slid 
along the coil, the thumb points constantly in the same direc- 
tion which is that of every line of force enclosed by the coil. If, 
therefore, instead of simply passing the wire by the needle, as in 
Oerstedt's experiment, we take a turn entirely around it, the de- 
flecting force is very much increased. Finally, we need not stop at 
one loop. Every succeeding turn adds its lines of force to those 
already in the field and we may, therefore, use a coil of a great 



ELECTRO-MAGNETICS. 275 

many turns and multiply by just so much the effects of the cur- 
rent. Such is the principle of Schweigger's multiplier (Fig. 158; 
which consists of a suitable frame which may be rectangular, oval 
or circular and around which are wrapped many turns of insulated 




Fig. 158. 

wire. The frame must be of some non-magnetic material such as 
wood, ebonite, brass, etc., otherwise it would acquire magnetism 
from the current. In the center of the coil is pivoted the needle 
whose deflection is to be observed. 

A multiplier should be used with feeble currents only. With a 
strong current it is not necessary; moreover, the resistance of the 
many turns of wire would cut down a large current. It is true 
that it also reduces a small current but not so much proportionally. 
The general rule is that a multiplier is used when the circuit 
already contains great resistance but should not be used if the 
resistance be small. 

366. Methods of Weakening Controlling Force. — The second 
method of rendering a needle more sensitive, the weakening of the 
controlling force, may be applied in two ways: 

(a) Hatiy's method. The earth's controlling -force may be 
very nearly neutralized, there being left a small excess just suffi- 
cient to control the needle. 

(b) Astatic combinations. The earth's controlling force may 
be entirely neutralized, and some very feeble force, such as the 
torsion of a silk fibre, substituted therefor. 

367. Haiiy's Method.— Haiiy's method of weakening- the oanh's 
control is shown diagrammatically in Fig. 159 as being applied bo 
the needle of Schweigger's multiplier. The needle is suspended in 



276 



ELEMENTS OF ELECTRICITY. 



the center of the multiplier, the plane of the coil being in the 
magnetic meridian. A brass rod AB projects upward from the 
top of the coil and upon this rod there slides a bar magnet NS, 
usually curved as shown. Now, as this bar magnet ic slid down 
towards the coil, its north pole repels with an increasing force the 




Fig. 159. 

north pole of the needle. A point is finally reached where NS 
exactly counterbalances the earth's controlling force upon the 
needle and if this point be passed the needle is reversed. By stop- 
ping the bar magnet just above this critical point, the effect of the 
earth's control may be reduced to a minimum. This method is 
employed in Thompson's mirror galvanometer (Par. 377). 

368. Astatic Combinations. — Two needles of equal size and 
strength fastened rigidly together in reversed positions and with 
their axes parallel constitute an astatic pair (Fig. 160). This com- 
bination is independent of the earth's control and the controlling 
force is generally the torsion of a fine silk fibre by which the needles 
are suspended. They are usually mounted so that the lower needle 
swings in the center of a multiplier, the upper needle travelling 
over a graduated scale on the top of the coil and thus serving as a 
pointer. Application of the right hand rule will show that the 



ELECTRO-MAGNETICS. 



277 



current in the portion of the coil between the two needles will 
cause them both to rotate in the same direction. By using a coil 
wrapped like a figure eight, both needles may be surrounded by 
coils. 




Fig. 160. 

There are a number of other astatic combinations. A suspended 
horseshoe magnet is astatic and may be used as an astatic pair. 

369. Magnetic Shells. — Should we be able to cut from the end 
of a bar magnet a thin slice, and should this slice preserve its 
original polarity, we would have a magnetic shell, a thin piece of 
metal, one face of which would be of north polarity, the other 
south. 

Another conception of a magnetic shell is to suppose that we 
had a great number of very small magnets, like minute type, and 
that we should arrange them over the area of a circle side by side 





Fig. 161. 

like the cells of a honeycomb (Fig. 161), the north poles all point- 
ing up, the result would be a magnetic shell. If a coil of wire be 
bent into a circle of the same size as the shell, a current could be 
sent through the wire which would produce inside the coil as many 
lines of force as emerged from the shell. Since we have shown (Par. 
365) that these lines all emerge from one face of the coil and in the 
same direction, the coil and the shell are magnetically equivalent 
to each other. Coils carrying a current behave in many ways as 



278 



ELEMENTS OF ELECTRICITY. 



if they were magnets. They have polarity and will attract or 
repel a magnet, depending upon the pole of the magnet and the 
face of the coil to which it is presented. They also attract or repel 
each other. 

This conception of a magnetic shell is used in mathematical dis- 
cussions of electricity. We will not have occasion to use it further 
but there follows from it a very important principle which we shall 
now develop. 

370. De La Rive's Floating Battery. — One form of De La Rive's 
floating battery is represented in Fig. 162. It consists of a turnip- 
shaped glass cell with a constricted lower part containing dilute 
acid. Upon a cork in the mouth of the cell is mounted a vertical 




Fig. 162. 

coil of wire of a number of turns, the ends of this coil extending 
below the cork and terminating, one in a copper, the other in a 
zinc plate which dip into the acid. The arrangement is therefore 
seen to be only a simple cell, the coil constituting the external cir- 
cuit. The cell is placed in a basin of water so that it floats freely. 
If the current flows around the coil in the direction indicated by 
the arrow, the lines of force of the coil pass through from right to 
left, or, from what we have just seen, the coil is equivalent to a 
magnetic shell whose north face is to the left. 

Suppose that, as represented in the figure, the north pole of a 
bar magnet be presented to the north face of the coil. The float- 



ELECTRO-MAGNETICS. 



279 



ing cell, as was to be expected, will back away or recede, but, more 
than this, it will turn around until its south face is presented and 
will then approach the magnet and, instead of stopping when it 
has reached the pole, will continue to advance and will thread 
itself upon the magnet until it has reached the middle point. Its 
lines of force and those of the magnet now coincide in direction. 
It is now in a position of stable equilibrium for if it be pushed 
towards either end of the magnet and released it will immediately 
return to its median position. On the other hand, suppose the 
coil to be held and the magnet thrust into it in reversed direction, 
that is, with its lines of force opposite in direction to those of the 
coil. If the coil be released when exactly at the center of the 
magnet it will remain, but it is in unstable equilibrium, for if dis- 
placed ever so slightly in either direction from this central position 
it will slip off the magnet, turn around and return. 

One of these cells floating freely in a vessel of water will finally 
come to rest with the axis of the coil in a north and south position, 
that is, with its field coinciding in direction with that of the earth. 
Two such cells will move about until the fields of their coils coin- 
cide in direction. 

371. Maxwell's Law.- — The principle in accordance with which 
the movements described in the preceding paragraph take place 




Fig. 163. 

has been formulated by Maxwell to the effect that every electro- 
magnetic system tends to change its configuration so that the exciting 
circuit will embrace in a positive direction the maximum number of 
lines of force. This law applies to all combinations of closed cir- 
cuits and magnetic fields, whether these fields be produced by 
magnets, by other circuits, or even by the circuit itself. This last 
is shown by an experiment devised by Ampere. In a wooden block 
(Fig. 163) there are hollowed out two parallel troughs which are 



280 



ELEMENTS OF ELECTRICITY. 



then filled with mercury. A wire bent as shown is then placed as 
a bridge with one end in each trough and floats on the surface of 
the mercury. The current entering at A crosses this bridge and 
leaves by B, the lines of force in this rectangular area all pointing 
up as shown by the arrows. As soon as the circuit is closed, the 
wire floats off towards C, thereby increasing the area ACB and 
consequently the number of lines of force embraced by the circuit. 
The majority of the instruments, shortly to be described, 
operate in accordance with this law and it also explains the move- 
ment of all motors. It has already been shown (Par. 144) that, 
in a more general form, it accounts for the position assumed by 
magnetic needle. 

372. Galvanometers. — A galvanoscope indicates by the move- 
ment of its needle both that a current is flowing and the direction 
of its flow. If this movement also affords a measure of the strength 

of the current, the instrument is 
called a galvanometer. There are 
many varieties of galvanometers 
but they may all be classed under 
one of two heads : first, those in 
which a needle moves in a field 
produced by a fixed coil and, 
second, those in which there is 
no needle but a suspended coil 
which swings in a fixed field. 
Of the latter class, the field may 
be produced by a permanent 
magnet or by a fixed coil. We 
shall now describe examples of 
each of the above. 

373. The Tangent Galvanom- 
eter. — This is an example of a 
galvanometer of the first class, 
that is, one with a needle mov- 
ing in a field produced by a fixed 
coil. It consists (Fig. 164) of a 
vertical circular coil, more than 
one foot in diameter, mounted upon a base by which it may be 
accurately placed in the magnetic meridian. The coil is composed 




ELECTRO-MAGNETICS. 281 

of a single turn of heavy copper wire or copper ribbon. For 
measuring small currents it may consist of many turns of fine 
wire. Pivoted at the center of this coil is a short thick needle, 
generally less than an inch in length. Since it would be very 
difficult to read with any accuracy a scale engraved upon a circle 
whose diameter is only one inch, the needle is usually prolonged 
by light aluminum pointers. These have no magnetic effect but 
permit the use of a much larger graduated scale. 

374. Measurement of Current by Tangent Galvanometer. — In 

order to measure a current by the tangent galvanometer, the latter 
is connected up in the circuit, its coil accurately placed in the mag- 
netic meridian, the circuit closed and the angle of deflection of the 
needle read. If it be convenient to reverse the current, this is done, 
the new angle of deflection read and the mean of the two readings 
is taken as the correct one. 

In Par. 146 we saw that "the magnetic field which, acting at 
right angles to the meridian, produces in a needle a deflection 8, is 
equal to the horizontal component of the earth's magnetism at that 
point multiplied by the tangent of the angle of deflection," or 

/=ff.tan« 

Again, in Par. 354 we saw that the field produced at the 
center of a circular coil of radius r by a current of / absolute 
units is 

J r 

We therefore have 



whence 



I 2ir TT 

■ = H . tan 5 



r 
I = cr ■ H . tan 8 



In this r is determined by measurement of the coil, H is 
obtained from observation (Par. 148), or from a table (Par. 175), 
8 is read from the galvanometer scale and tan 8 is obtained from a 
table. 

If the galvanometer coil has n turns, the second expression for / 

becomes / = ■ . The factor — , since it depends purely 



282 ELEMENTS OF ELECTRICITY. 

upon the dimensions of the instrument, is called the galvanometer 
constant. Calling this G, we have 

f=I.G 

whence, if / = 1, f=G, or the 
galvanometer constant is equal to the strength of the field pro- 
duced at the center of the coil by a current of one absolute unit. 

In practice, it is more frequent to use the tangent galvanometer 
to compare currents rather than to determine them absolutely. 
Various currents are to each other as the tangents of the angles of 
deflection which they severally produce. If the deflection pro- 
duced by a known current be ascertained, the determination of 
other currents is a simple matter. 

375. Remarks on Principle of Tangent Galvanometer. — The 
deduction in the preceding paragraph is based upon two assump- 
tions, neither of which is strictly accurate, although the error is 









i i i 
i i i / 



i ,. 



-j — ;- -|-h!-j j , Ttff^; ; ) ; ) > j 



\ 
\ 



Fig. 165. 

usually negligible. First, the deflecting force is supposed to be 
perpendicular to the meridian. Fig. 165 represents the field along 
the horizontal diameter of the coil of a tangent galvanometer, 
whence it is seen that the lines of force are curves and therefore 
are perpendicular to this meridian only where they pierce the 
plane of the coil. They have, however, less curvature near the 
center of the field and this flatness increases with the diameter of 
the coil, for which reason the needle is made very short and the 
coil large. A still better remedy is to use two parallel coils and 
place the needle midway between them. The lines of force of the 
field in this case are sensibly parallel. This requires use of gen- 
eral expression, Par. 354, instead of that for field at center of coil. 
Second, the expression employed for the intensity of the field is 
determined for the center of the coil (Par. 354). The field, as in- 



ELECTRO-MAGNETICS. 



283 



dicated in the figure, is much stronger near the coil and diminishes 
towards the center. The needle is therefore made short so that 
its poles do not extend into a field much stronger than that at the 
actual center. 

376. The Sine Galvanometer. — The sine galvanometer, shown 
in its simplest form in Fig. 166, differs from the tangent gal- 
vanometer only in that the coil need not be so large and that 
the needle extends as nearly across the diameter of the coil as its 




Fig. 166. 



surrounding graduated circle will permit. The poles of the needle 
therefore lie in the strong field close to the coil and the instrument 
is more sensitive than the tangent galvanometer. The coil is free 
to rotate about a vertical axis and in more improved forms of the 
instrument there is a horizontal graduated limb from which may 
be read by a vernier the exact angle through which the coil has 
been turned. This limb, however, is not essential. 

To use the instrument to measure a current, it is connected up 
in the circuit and accurately adjusted until the coil lies in the mag- 
netic meridian. The horizontal graduated limb is then read and 
the circuit is closed, causing a deflection of the needle. The coil 
is then turned by hand in the direction of the deflection of the 



284 ELEMENTS OF ELECTRICITY. 

needle until the needle is overtaken and lies once more in the plane 
of the coil. The deflecting force, or the field of the coil, is now per- 
pendicular to the needle. The angle through which the coil has 
been turned is read from the scale on the horizontal limb. Should 
there be no horizontal limb, this angle can still be determined, for 
it is only necessary to take the reading of the needle, then break 
the circuit and take the reading of the needle when it has swung 
back into the meridian; the difference between these two readings 
is the required angle. 

In Par. 147 it was shown that "magnetic fields acting at a 
constant angle with the needle are to each other as the sines of the 
respective angles of deflection." It follows that the current is 
proportional to the sine of the angle through which the coil has 
been turned; also, that different currents are to each other as the 
sines of these angles. The sine galvanometer can therefore be 
used to compare currents although it can not be used, like the 
tangent galvanometer, • to measure currents absolutely. 

Should the deflecting force be greater than the controlling force, 
the coil will never overtake the needle, and in such a case the 
instrument can not be used. 

377. The Mirror Galvanometer. — The mirror galvanometer is 
an extremely sensitive form of instrument and is more frequently 
used as a galvanoscope than as a galvanometer, in fact, it was 
devised by Lord Kelvin to give indications of the exceedingly small 
currents transmitted by submarine cables. Its principle will be 
understood from Fig. 159. It consists of a vertical coil of many 
thousand turns of very fine insulated wire. The opening through 
the coil is barely half an inch in diameter and in the center of this 
there hangs, by a silk fibre, a very light glass mirror, about the 
size of a silver ten-cent piece. The mirror is slightly concave so as 
to focus in a long pencil any rays of light which fall upon it. To 
the back of this mirror there are glued three or four very light 
magnets made of short sections of watch spring. The controlling 
force of the earth's magnetism is neutralized by Haiiy's method. 
The little mirror normally hangs with its plane parallel to the 
face of the coil, but when a current passes through the coil the 
magnets at the back of the mirror tend to turn in accordance with 
Maxwell's law until their lines of force coincide with those of the 
coil. A beam of light is caused to fall upon the mirror and is 
reflected back, producing a bright spot upon a blank wall or upon 



ELECTRO-MAGNETICS. 



285 



a suitably-prepared scale. The slightest angular motion of the 
mirror is revealed at once by motion of the spot of light, the 
angular motion of the spot being twice that of the mirror and 
the radius being the distance from the mirror to the wall or scale. 
Thompson states that the most improved form of this instrument 
gives indications of a current as small as one fifty -four-thousand 
millionth of an ampere. 

378. Suspended Coil Galvanometer. — In the galvanometers 
described in the preceding paragraphs, the coil carrying the cur- 
rent is fixed and the magnet rotates; in the form now to be de- 
scribed the magnet is fixed and the coil rotates. While not having 
the extreme delicacy of the mir- 
ror galvanometer, the suspended 
coil galvanometer is still of a high 
order of sensitiveness and is used 
by practical electricians where the 
most refined observations are re- 
quired. There are many different 
forms and it is known by other 
names, such as the D'Arsonval 
galvanometer, the reflecting gal- 
vanometer, etc., but the principle 
of all is the same. 

A usual form consists (Fig. 167) 
of a heavy rectangular frame 
of magnetized steel whose poles 
are N and S. This frame is 
mounted upon a wooden back C 
which may be fastened to a wall, 
mounted upon a tripod, or other- 
wise suitably supported. Through 
the center of the top of the frame 
is bored a hole into which is 
screwed a vertical brass tube D. 
In the upper end of this tube 
there fits a small brass spindle 
with a cross-bar handle E. This spindle may be turned about a 
vertical axis and may be raised or lowered and fastened in any 
desired position by the set-screw shown at the right. The mov- 
able coil is suspended from the spindle by means of a very delicate 




286 ELEMENTS OF ELECTRICITY. 

phosphor-bronze filament. Silk or quartz fibres can not be used 
since the suspension must convey current to the coil. The 
coil, which swings in the space between the poles, consists of 
many turns of very fine wire wrapped upon a thin, light, 
elongated rectangular metal frame. Midway between the poles 
N and S there is fastened to the wooden back C a vertical 
soft-iron cylinder K which projects into the opening of the coil 
frame, almost entirely filling this space and leaving barely room 
for the coil to turn. This, as shown in Fig. 69, Par. 143, greatly 
concentrates the field in which the coil moves. Above the coil 
frame and supported by it is a small mirror F. Below the coil, a 
coiled phosphor-bronze filament connects to a small metal bracket 
G which in turn is connected from behind to the binding post B. 
The other binding post A is connected direct to the steel frame. 
A current entering at A travels up the steel frame to the brass 
tube, thence up this tube to the spindle, thence down the suspen- 
sion to the coil, around the coil, thence through the lower filament 
to G and out by B. The coil hangs normally with its face to the 
front, the controlling force being the torsion of the phosphor- 
bronze suspension. If the coil does not hang properly, it can be 
made to do so by turning the spindle E. With the poles situated 
as represented in the figure, the lines of force of the field run from 
right to left. When a current flows through the coil, the lines of 
force of the coil are from front to rear, or the reverse; therefore, 
the coil, in accordance with Maxwell's law, turns either to the 
right or left. The coil, mirror and filaments are protected by a 
metal plate screwed to the frame and carrying a glass window 
through which the mirror may be observed. 

In using the instrument, there is attached to the hooks H H an 
arm (Fig. 168) which carries at its farther end a telescope and a 
printed scale. The scale, which is usually divided into millimeters, 
is one-half meter from the mirror. By means of the telescope the 
reflection of the scale in the mirror is observed. Since the tele- 
scope inverts objects and the mirror reverses them right for left, 
the numbers on the scale must be engraved both upside down and 
reversed. Cross hairs in the telescope allow the scale to be read 
very accurately. When the coil, and consequently the mirror, is 
deflected by a current, it appears to the eye of the observer as if 
the scale moved across the field of the telescope. For moderate 
deflections of the coil the currents producing these deflections are 



ELECTRO-MAGNETICS. 



287 



proportional to the number of scale divisions passed over by the 
vertical hair. 




Fig. 168. 



379. Damping. — In instruments in which readings are taken of 
the angular displacement of a needle, a coil, or a mirror, the mov- 
ing part may oscillate for some time before coming to its final 
position of rest. This causes, in taking observations, a vexatious 
delay which it is very desirable to avoid. Any process by which, 
while not interfering with the freedom of movement of the part, 
it is made to come to rest quickly is called "damping," and an 
instrument whose needle moves at once to the proper reading on 
the scale is said to be "dead beat." Damping may be brought about 
by (a) mechanical means or (b) electrical means. As an example 
of mechanical damping, a moving coil may have suspended below 
it a metal vane which is immersed in oil, the viscosity of the liquid 
slowing down the movement and preventing vacillation. Sus- 
pended coil galvanometers often have attached to the mirror a 
thin sheet of metal or mica which turns in a little closed box which 
it nearly fits. The confined air in this box acts something like the 
oil in the first case. 

Electrical damping can not be thoroughly explained at present 
but depends upon the principle that a piece of metal moved in a 
magnetic field experiences forces which tend to stop the movement 
(Par. 430). This is the method employed in the suspended coil 
galvanometer just described. The metal frame upon which the 
coil is wrapped turns in the strong magnetic field between the poles 
and the soft-iron core and is thus brought quickly to rest. 



288 ELEMENTS OF ELECTRICITY. 

380. Need of Galvanometer Shunts. — The currents which a 
reflecting galvanometer may measure are extremely small. Thus, 
if a pin be connected by a wire to one terminal of the galvanometer 
and a needle be connected to the other and the pin and needle be 
held tightly between the fingers, the contact of the two dissimilar 
metals with the slight moisture of the fingers will drive a sufficient 
current through the coil to cause the mirror to run entirely off the 
scale. In order therefore to measure even minute currents we must 
employ a shunt by which, as explained in Par. 301, only one-tenth, 
one-hundredth, or one-thousandth of the total current is permitted 
to flow through the instrument. Even in this case it is usual to 
insert in the circuit a resistance of 50,000 or 100,000 ohms by 
which the current is reduced to measurable intensity. 

381. The Universal Shunt.— We saw in Par. 301 that the resist- 
ance of a galvanometer shunt must bear a fixed relation to the re- 
sistance of the galvanometer with which it is used and that shunts 
are not interchangeable and can be used only with the galvanom- 
eter for which they are constructed. The phosphor-bronze sus- 
pension of a suspended coil galvanometer is frequently broken and 
must be replaced by a new one, in doing which the resistance of 
the galvanometer is usually considerably changed and this change 
would render useless a shunt designed to accompany the original 
resistance. Reflection will show, however, that if we simply wish 
to compare currents relatively it is not necessary to know what 
fraction of the total current flows through the galvanometer, for 
if 1/xth of a current /' flowing through a galvanometer produces 
a certain deflection, and if 1/xth of a different current I" produces 
a deflection twice as great, then the current I" is twice as great 
as the current /'. 

Carrying out the idea farther, Ayrton devised a universal shunt 
which may be used with any galvanometer and which can be so 
varied that, irrespective of the resistance of the galvanometer, the 
deflection produced is proportional to one- tenth, one-hundredth, 
or one-thousandth, etc., of the total current. This shunt is shown 
diagrammatically in Fig. 169. Five contacts (sometimes six) are 
arranged in the arc of a circle and marked, 1, T V, T ^, T oV o an d 0. 
Between these contacts are resistance coils A, B, C, D. If R be 
the total resistance, A is .9 of R, A + B is .99 of R and A + B+C 
is .999 of R. A common arrangement of these resistances is to have 
A = 9000, B = 900, C = 90 and D = 10 ohms, a total of 10,000 ohms. 



ELECTRO-MAGNETICS. 



289 



The current enters by K and leaves by H. The arm attached to 

K can be placed on any desired contact. The galvanometer is 

connected in shunt with the total resistance as shown. Let the 

resistance of the galvanometer be x. With the arm on contact 1, 

let the total current be /, and the current through the galvanom- 

Rx 
eter be I g . The joint resistance from K to H is p (Par. 293). 




Hence 



Whence 



j T _ Rx 



: x 



I = L 



R + x 
R 



Suppose the arm to be placed on the 
resistance from K to H is now 



Tty«j 



(I) 
contact. The joint 



(.99jR.+ a?)(.01fl) _ (.99R + x)(.01R) 



99R + X+ MR 



R + x 



If the total current be now /' and the current through the 
galvanometer be I' g 

= (.99fl + ,)(.01g) 

R + x 



290 



ELEMENTS OF ELECTRICITY. 



Hence 



From (I) and (II) 



/' 



JVioo 



R + x 
R 



T :I = 100F g :I g 



(ID 



(III) 



Or if D be the deflection produced by the first current and D' 
that produced by the second 

V : 7=100. D f :D 

or the ratio of the total 
current when the arm is on the T ^o contact, to the total current 
when the arm is on the 1 contact, is as one hundred times the de- 
flection produced in the first case, is to the deflection produced in 
the second case. 

It will be noted that x, the resistance of the galvanometer, does 
not appear in (III), hence the shunt may be used with any galva- 
nometer. 

a 




Fig. 170. 

382. Weber's Electro -Dynamometer. — This instrument, an ex- 
ample of a galvanometer of the second class (Par. 372), that is, one 
in which a coil swings in a magnetic field produced by other coils, 
is shown diagrammatically in Fig. 170. It consists of two large 
parallel coils A and B mounted so that they have a common axis 



ELECTRO-MAGNETICS. 29 1 

and their planes are vertical. Midway between these there hangs 
by a bifilar suspension (Par. 127) a small coil C so arranged that 
its axis is in the same horizontal plane but at right angles to the 
common axis of A and B. As generally used the same current 
traverses all three coils. Entering at E it flows around the coil A 
and out to F, thence by the wire to G, thence down the slender 
wire suspension to C, around this coil, up the other suspension to 
H, down to D, around the coil B and finally out by K. 

If the currents in the two coils flow as indicated by the small 
arrows, the field of AB will be from right to left; that of C from 
rear to front and therefore C, viewed from above, takes up a clock- 
wise motion, or, in accordance with Maxwell's law, tends to turn 
so that its field coincides in direction with the field of AB. The 
angle of deflection is read, as in the mirror galvanometer, by means 
of a small mirror attached to the suspended coil. The controlling 
force is gravity which tends to pull the inner coil back to its pri- 
mary position; the moment of this force being directly proportional 
to the sine of the angle of deflection, or 

M c = a . sin 8 

The deflecting force is due to the interaction of the fields of the 
suspended and the fixed coils and since these fields are severally 
proportional to the currents flowing in the coils (Par. 354), the 
deflecting force is proportional to the square of the current. The 
moment of the deflecting force is proportional to the product of 
the square of the current and the cosine of the angle of deflection, 
or 

M d = b.P.cos>8 

When the coil comes to rest the two moments are equal and 
opposed, hence 

b.P. cos 8 = a . sin 5 
whence 

I 2 =^.tan5 
b 

or, the square of the cur- 
rent is proportional to the tangent of the angle of deflection. This 
fact might have been anticipated since reflection will show that 
the instrument is virtually a tangent galvanometer. 

In making an actual observation a number of refinements must 
be observed in determining the constants a and b above, and it 
may also be necessary to allow for the effects of the earth's field. 



292 



ELEMENTS OF ELECTRICITY. 



Should the current through the instrument be reversed in direc- 
tion, the fields in the coils will also be reversed but from the figure 
it will be seen that the tendency will still be for the movable coil 
to turn in a clockwise direction. Since this direction of deflection 
does not vary with reversal of the current, instruments of this class, 
that is, two-coil instruments, are employed in the measurement of 
alternating currents, or those currents which reverse many times 
per second. 

383. Siemen's Electro-Dynamometer. — Siemen's electro-dyna- 
mometer, shown diagrammatically in Fig. 171, is in principle the 




same as Weber's but differs in that the movable coil is external 
to the fixed, and that the controlling force is the torsion of a deli- 
cate coiled spring. The base and supporting upright are of wood. 
There are two fixed coils, one of a few turns of heavy wire for use 
with large currents, the other of many turns of a finer wire for use 
with smaller currents. The short coil is wrapped upon the long 



ELECTRO-MAGNETICS. 293 

coil. The terminal for one of these coils is the binding post A, that 
of the other coil the binding post B, and the remaining end of each 
coil is connected to the metal bracket D which at one end carries 
a little cup of mercury. One terminal of the movable coil dips 
into this; the other terminal dips into a similar cup just below the 
first, this last cup being connected by a wire to the binding post C. 
The movable coil is suspended either by a silk fibre or upon a 
pivot and is free to rotate about a vertical axis. It carries a needle 
or pointer which is bent over the edge of an upper circular scale. 
This scale may be graduated in degrees but more often in some 
arbitrary number of points, such as 400. If the current in the coils 
flow as indicated by the arrows, the field of the fixed coil is from 
left to right, that of the movable coil from rear to front and, 
viewed from above, the rotation of the movable coil is counter- 
clockwise. This movement is opposed by the torsion of the spiral 
spring attached to the upper part of the movable coil and by 
means of a projecting pin or stop is restricted to a few divisions 
of the graduated scale. At the center of this scale there is a milled 
head to whose end the upper end of the coiled spring is attached. 
Below the milled head there is a second pointer which, as the head 
is turned, sweeps around the graduated circle and indicates the 
angle through which the head has been turned. 

When a current is flowing through the instrument, the movable 
coil is urged in a counter-clockwise direction. The milled head is 
turned in a clockwise direction and the torsion of the spiral spring, 
which varies directly as the angle through which the milled head 
is turned, tends to drag the coil back to its primary or zero position. 
When the coil has finally been brought back to this position, the 
pull exerted by the spring exactly balances the contrary moment 
exerted by the current. 

Consider a vertical portion of the wire in the movable coil and 
an adjacent portion in the fixed coil. The force exerted between 
these portions is directly proportional to their length, to the prod- 
ucts of the currents flowing in them, and inversely proportional 
to the simple distance between them (Par. 362). The length of the 
portions is constant, so also is the distance between them, since 
the coil is always brought back to its original position, therefore. 
the force between the portions, and consequently the force be- 
tween the coils themselves, varies as the square of the current and 
also as the number of divisions of the scale over which the pointer 



294 ELEMENTS OF ELECTRICITY. 

attached to the milled head has been turned. From this it follows 
that the current varies as the square root of the angle of torsion, or 

I=KV~8 

8 being the number of divi- 
sions of the scale indicated by the pointer. The constant K is 
different for different instruments but is easily determined by 
passing through the instrument a known current / and noting the 
corresponding torsion 5. 

In addition to its use in measuring currents, this instrument, as 
will be shown later (Chap. 36), may be used to measure electrical 
power. 

384. Ballistic Galvanometer. — In the earlier attempts to meas- 
ure the velocity of moving projectiles, use was made of a piece of 
apparatus called a ballistic pendulum. This consisted of a large 
pendulum with a very heavy and solid bob. The projectile was 
fired against and embedded itself in the bob, the blow causing 
the pendulum to swing through a certain angle which was recorded. 
Knowing this angle, the vertical height through which the weight 
had been lifted could be determined and, knowing the weight of 
the projectile, the velocity with which it struck the pendulum 
bob could be calculated. 

When a charged body is discharged through a conductor, the 
charge in its passage is a veritable current but its duration is only 
momentary. If passed through a galvanometer, it gives to the 
moving parts a sudden impulse or blow comparable to the blow 
given to the pendulum by the bullet. If these moving parts be 
somewhat heavy and therefore rather slow in vibration, the cur- 
rent will have passed before any appreciable movement takes 
place. It can be shown that the sine of half of the angle of the 
first swing or "throw" of the needle is proportional to the charge 
which has passed through the coil. (See Gray, Absolute Meas- 
urements in Electricity, Vol. II, pp. 390-396.) Galvanometers 
used in this manner are called ballistic galvanometers. They are 
generally of the suspended coil type and must not be damped. 



ELECTRO-MAGNETICS, 295 



CHAPTER 31. 

ELECTRIC MAGNETIZATION OF IRON AND STEEL. 

385. Solenoid. — A cylindrical coil of wire whose length is great 
as compared to its diameter is called a solenoid, the Greek word 
solen meaning a tube. The successive turns of the coil are wrapped 
as closely together as the thickness of the insulating covering will 
permit but in diagrams it is usual, for the sake of clearness, to 
represent these turns as somewhat widely separated. To give an 
accurate shape to the coil it is generally wrapped upon a material 
core, such as a wooden rod or a tube of glass or paper, which after- 
wards may be withdrawn. In diagrams, to avoid confusion as 
to the direction in which the coil is wrapped, it is preferable to 
represent the core as in position. 

The coil being a helix, the turns are inclined to the axis of the 
cylinder but each is electrically equivalent to a turn at right angles 







urn 

Fig. 172. 

to the axis (Fig. 172) and a short portion parallel thereto and equal 
in length to the pitch of the coil. The effect of these longitudinal 
portions is neutralized if one end of the coil be brought back along 
the axis of the coil, or if the wire, the circular direction of its wind- 
ing being unchanged, be wound back to the starting point, thus 
forming a second layer on top of the first. 

386. A Solenoid Equivalent to a Bar Magnet. — If a current be 
passed through a solenoid, application of the right hand rule will 
reveal the fact, which indeed has already been shown (Par. 365\ 
that the successive turns combine in the production of a field in the 
same direction. Thus (Fig. 173), all the lines of force inside of 
the solenoid run in the direction shown by the long arrow. A 
solenoid carrying a current is therefore magnetically equivalent 



296 ELEMENTS OF ELECTRICITY. 

to a bar magnet. It has poles, it will attract magnetic sub- 
stances, it will attract or repel the pole of a bar magnet and, if 



N 




\ 



Fig. 173. 

freely suspended, it will turn so as to place itself in the magnetic 
meridian. 

387. Intensity of Field on the Axis of a Solenoid. — The inten- 
sity of the field at a point on the axis of a circular coil is (Par. 354) 

H = *£ dynes (I) 

in which / is the current in 
absolute units, r is the radius of the coil, and x is the slant distance 
from the coil to the point on the axis. 

Let P, Fig. 174, be a point on the axis of a solenoid through 
which a current J is flowing. If in each centimeter length of the 

A B 

OOOOOO -^Q o op.o o o o o 



OOOOOO ooooooooo 

Fig. 174. 

solenoid there be N turns, we may consider that around such 
unit of length there is flowing a sheet of current of strength NI. 
The current over a small portion A B is therefore proportional to 
the length of AB or N.I.dl. 

Since - = sin 6, expression (I) can be written 

H = — y~ sm dynes 

The field at P due to the current on AB is, therefore, 

, ,, 2irNI.dl.r . . , TTX 

dH= - 9 sm 6 (II) 



ELECTRO-MAGNETICS. 297 

From the figure, ^ = dd, or AE = AP.dd (III) 

From the similar triangles AEB and £PF 
AE : AB = BF : BP 

Hence A£ = AE ^ ^ BP (IV) 

or, substituting from (III) 

AB = AP.dd. - 
r 



AB = dl=-dd 
r 



and as AB decreases, AP approaches BP, hence 

Substituting in (II) 

dH=2irNI. smd.dd (V) 

Integrating 

H = 2irNI( — cos 0)+ a constant 

The field due to the entire solenoid is obtained by taking this 
expression between the proper limits. If P be at the center of the 
coil and if the coil be so long that = 0° and 180°, then 

H = 4:wNI dynes 

If P be at the mouth of the solenoid so that is 0° and 90°, 

H=2tNI dynes 

or the field at the mouth 
of a long solenoid is one-half what it is at the center. 

It is to be noted that since in these expressions for the field the 
radius of the coil does not occur, the intensity of the field would 
appear to be independent of the diameter of the solenoid. This, 
however, is not correct unless the further condition be expressed, 
a condition already introduced by the assigned values of in the 
integration, that the various solenoids are geometrically similar. 
Should the radius of the solenoid be doubled or trebled, its length 
must be likewise doubled or trebled. 

The length of wire required in similar solenoids varies as the 
square of their like dimensions and if the length be increased 
the diameter of the wire must be increased to overcome the in- 
crease in resistance, therefore, considerations of economy lead us 
to make the coil fit its core as closely as possible. 



298 ELEMENTS OF ELECTRICITY. 

It has been shown that the field at the center of a long solenoid is 
very uniform. If the solenoid be wrapped upon a circular core, so 
as to return upon itself, the field at every cross-section is the same. 

388. Ampere Turns. — In the discussion in the preceding para- 
graph the current / is in absolute units. If it be given in amperes 
it must be reduced to absolute units by dividing by ten. The 
expression for the field at the center of a long solenoid becomes in 

this case a 

H=^.iV./dyne£ 

If the length of the coil be I and if the total number of turns 
be n f this may be written 

H = .n .1 dynes 

10./ 

The field therefore varies with nl. This product remains a 
constant if n and I vary reciprocally, hence three amperes mak 
ing five turns produce the same magnetic effect as five amperes 
making three turns, or as one ampere making fifteen turns, or as 
fifteen amperes making one turn. In any coil the product of the 
total number of turns times the current flowing in the coil is called 
the ampere turns, and this product appears as a factor in all ex- 
pressions dealing with circular coils. We have already employed 
it in the discussion of the tangent galvanometer (Par. 374). 

389. Variation of Field of Solenoid with Current. — The fact 
that the field on the axis of a solenoid varies directly with the 





current may be shown experimentally as follows. In Fig. 175, S 
represents a solenoid, B a battery, K a key, R a rheostat (Par. 
302), A an ammeter (a current-measuring instrument), and G a 
galvanometer with a short needle and long attached pointers 
poised over a graduated circle and placed so that the axis of the 



ELECTRO-MAGNETICS. 299 

solenoid prolonged passes through the pivot of the needle and is 
perpendicular to the magnetic meridian. By means of the rheo- 
stat, the current through the solenoid may be varied at will. The 
strength of the current is read direct from the ammeter. When 
the key K is closed, permitting a current to flow, the needle of the 
galvanometer is deflected. It will be seen that this is the case 
discussed in Par. 146 and that the deflecting force (which is due 
to the field of the solenoid) varies as the tangent of the angle of 
deflection. If, therefore, we lay off on a horizontal axis distances 
proportional to the current through the solenoid, the correspond- 
ing ordinates laid off proportional to the tangent of the angle of 
deflection will be proportional to the corresponding field. The 
points so determined will lie on a straight line passing through 
the origin (see OA, Fig. 176). 

390. Effect of Material of Solenoid Core Upon the Field.— With 
the apparatus described in the preceding paragraph we may in- 
vestigate the effect produced upon the field by varying the material 
of which the core of the solenoid is composed. Using cores of 
glass, rubber, wood, lead, copper, tubes of various gases or liquids 
or even vacuous space, no perceptible variation of the field is 
discovered, its strength remaining the same as when the solenoid 
enclosed only air. If, however, we insert a core of steel, the deflec- 
tion of the galvanometer needle will indicate that the field has 
been increased several hundred times, that is, there are now several 
hundred times more lines of force traversing the solenoid than 
there were before the steel core was inserted. If the core be of 
soft iron, the increase is still greater ; if it be of nickel, it is less than 
in the case of steel but much greater than in the case of air. 

391. Permeability. — The great increase in the density of the 
magnetic flux (number of magnetic lines) when iron is inserted in 
the coil has been explained by saying that iron is more permeable, 
or has greater permeability than the other substances. When a 
beam of light falls upon a sheet of clear glass many more rays go 
through than when the beam falls upon a sheet of dark glass. We 
may consider that in each case there is a force tending to drive the 
rays through and that the dark glass offers greater resistance while 
the clear glass offers less, or is more permeable. So also there is a 
magnetizing force which tends to drive magnetic lines through 
the field of the solenoid. Air, wood, etc., offer a magnetic resist- 



300 ELEMENTS OF ELECTRICITY. 

ance to this force and only a certain number of lines get through; 
iron and steel offer much less resistance, or are much more per- 
meable, and permit many more lines to pass. To this magnetic 
resistance the name reluctance has been given. It follows that 
reluctance is the reciprocal of permeability or that the two are 
comparable to resistance and conductance, respectively. 

392. Expression for Permeability. — We have seen that the field 
of a solenoid varies directly with the number of ampere turns per 
unit of length. It follows that the magnetizing force varies in 
the same manner, hence we may use H or 1.25 times these ampere 
turns (Par. 388), as a measure of the magnetizing force. If the 
magnetizing force which produced H lines per square centimeter 
in air produces B lines per square centimeter in iron, then the per- 
meability of the iron is Bj H. The accepted symbol for perme- 
ability is the Greek letter mu, //, hence 

B 

Hopkinson found that a magnetizing force which produced 10 
lines of force per square centimeter in air produced 12,400 per 
square centimeter in a specimen of wrought iron; the permeability 
of the iron was therefore 1,240. 

The permeability of air, glass, and other non-magnetic sub- 
stances is unity; that of bismuth, the most diamagnetic substance, 
differs from unity in the fourth place of decimals only. 

393. Magnetic Saturation. — The conception of permeability as 
outlined in the preceding paragraphs loses some of its definiteness 
when it is found that for magnetic substances it is not a constant 
but is different for different magnetizing forces. 

In Par. 389 it was stated that the field of a solenoid varies 
directly with the current. This is shown by the line OA in Fig. 
176, in which the abscissae are laid off proportional to the magnet- 
izing current and the ordinates proportional to the corresponding 
field. If we now insert in the solenoid a long soft-iron core, mag- 
netically neutral, and gradually increase the current, we will notice 
three stages in the field produced : (a) for small values of the cur- 
rent it will increase slowly; (b) as the current is increased it will 
rise suddenly until a certain point is reached, after which (c) it will 
continue to increase but slowly. These stages are shown graphi- 
cally in the curve OD. Since this curve represents the field pro- 



ELECTRO-MAGNETICS. 



301 



duced by the solenoid and the core in conjunction, if we subtract 
from its ordinates the corresponding ordinates of OA, we will get 
the curve of magnetization of the core alone. The result is the 
curve OE. The upper portion of this being very nearly parallel to 




MAGNETIZING 
Fig. 176. 



FORCE 



the horizontal axis indicates that the magnetization of the core 
would be but slightly increased by a further increase in the 
magnetizing current; in other words, the core is now magnetically 
saturated. 

394. Curves of Magnetization. — As will shortly be shown, the 
designer of electrical machines and apparatus is frequently called 
upon to solve problems such as the following: Given an iron core 
of a certain size, shape and quality; required the number of ampere 
turns to produce in this core a flux of a certain strength. Among 
the data needed for the solution is not simply the permeability of 
the particular kind of iron of which the core is constructed but its 
permeability when the magnetic flux is of the strength called for 
in the problem. Such information is contained in tables but is 
more striking when presented graphically in the form of curves of 
magnetization. Fig. 177 represents these curves for five different 
qualities of iron and steel, whence it is seen that soft annealed iron 
may be both most easily and most highly magnetized and that 
hard steel is most difficult of magnetization. From the figure it 
is seen that for a magnetizing force of 5 the magnetization of soft 



302 



ELEMENTS OF ELECTRICITY. 



iron is 10,000, or the permeability is 2000, while for a force of 50 
the magnetization is 16,000, or the permeability is only 320. 

It will be noted that these curves all exhibit the three stages as 
described in Par. 393. 



15,000 



AN HEM-E j 'RON 



10.000 /- 



£000 




IS %0 Z$ 30 35 40 
Fig. 177. 

395. Ewing's Theory of Molecular Magnetism. — The accepted 
explanation of these phenomena is that advanced by Ewing and 
has already been given in part in Par. 153. The molecules of mag- 
netic substances are inherently magnets but ordinarily exhibit no 
magnetic effects since they are grouped so as to mutually satisfy 
their individual polarities. Application of a magnetizing force 
disturbs this grouping, and exercises a directive effect upon the mo- 



/ 



/ 



X 



b 

Fig. 



178. 



lecular magnets, causing them to take approximately a common 
direction so that they combine in the production of a magnetic 
flux. His theory, as the following will show, satisfactorily ac- 
counts for the three stages in the curves of magnetization. Let us 
take the simplest possible hypothetical case, that of two molecular 
magnets, and let the two small needles in a, Fig. 178, represent 
these molecules. If they be remote from other magnetic bodies 



ELECTRO-MAGNETICS. 



303 



they will take up a position of equilibrium with their axes lying 
upon a common line. Let them now, as shown in b, be subjected 
to a magnetizing force H. If H be feeble the needles will move 
slightly but will not swing entirely to the right because they are 
pulled back by their mutual attraction. However, as H increases, 
this attraction will finally be overcome and the needles will then 
whirl suddenly to the right as shown in c. This corresponds to the 
stage of saturation. The needles, because of their action upon 
each other, are not strictly parallel nor can they ever become so. 
Further increase of H can only pull them a little more nearly 
parallel. If the magnetizing force be discontinued, the needles 
will not fly back at once to their original position but will linger 
and may require a slight jar to cause them to turn back. 

Ewing's theory has been corroborated experimentally. A great 
many small magnetic needles were distributed side by side upon 
a long board which was then inserted in a coil and the needles 
allowed to come to a position of equilibrium. The arrangement 
was then subjected to a gradually increasing magnetizing force 
and the resulting fields were determined and plotted as described 
above. The result was a curve showing the three stages of the 
usual magnetization curves. Furthermore, when subjected to a 
demagnetizing force the curve went through the cyclic changes 
described in the following paragraphs. 

396. Hysteresis. — Suppose that beginning with a magnetically 
neutral specimen of soft iron and apply- 
ing a gradually increasing magnetizing 
force we should determine and plot the 
corresponding curve of magnetization. 
Suppose that having reached a point 
where a magnetizing force OD (Fig. 179) 
produces a magnetization DA, we should 
reduce the magnetizing force to zero. It 
will be found that the magnetization is 
by no means reduced to zero but persists 
or lingers after the withdrawal of the 
force and has some such value as OC. 
That portion of the curve representing 
the change from A to C is concave to the 
horizontal axis. If now the magnetizing force be reapplied, the 
curve of magnetization will not retrace the path A NC but there 



B 


R^- 








IS-"" 


77 l 




K 


^"fp 








\f^j i 


A 




C 


/^m J 









^|f 


33 


H 



Fig. 170. 



304 ELEMENTS OF ELECTRICITY. 

will be a tendency for the magnetization to linger at the value 
OC and it will increase at first at a slower rate than it decreased, 
the corresponding portion CM A of the curve of magnetization 
being convex to the horizontal axis. If at some other point E 
the magnetizing force be again reduced to zero and then reapplied, 
a similar loop EQ KPE will be traced, and so on, the magnetiza- 
tion always holding back or conforming reluctantly to the changes 
in the magnetizing force. To this phenomenon the term hysteresis, 
a lag or lagging, is applied. 

397. Further Data on Permeability. — The magnetizing force 
OF, Fig. 179, produces the various degrees of magnetization cor- 
responding to FG, FM, FN, FP, FQ, FR, etc. Which of these is 
to be taken in determining the permeability of the specimen? It 
is seen that the notion of permeability is even more indefinite than 
was pointed out in Par. 393, and that in order that it may be of 
any practical use we must know the previous magnetic history 
of the specimen with which we are dealing. It can easily be shown 
that even though a specimen be magnetically neutral, its perme- 
ability, if it has recently been demagnetized by a single reversal 
of the current, is very different from what it is if it has never been 
magnetized at all. The usual understanding, therefore, is that 
when the permeability of iron or steel of a certain quality is given, 
it refers to a specimen which has not previously been magnetized 
and, furthermore, the permeability has been determined by the 
application of a continually increasing magnetizing force without 
reversals. 

398. Cycle of Magnetization. — If a specimen of soft iron be 
magnetized, then demagnetized, then magnetized to an equal 
degree in the opposite direction, then demagnetized, and finally 
again subjected to the original magnetizing force, it will pass 
through a cycle of magnetization represented by the curve in Fig. 
180. When the magnetizing force has first been reduced to zero 
the magnetization of the specimen is still proportional to OC. In 
order to remove this residual magnetism an opposite or negative 
magnetizing force OF must be applied. Since after the with- 
drawal of the magnetizing force the iron still retains a portion 
of the magnetism, we may say that the iron clings to this 
magnetism with a force equal to the force OF which must be 
employed to cause its relinquishment. The force which must 



ELECTRO-MAGNETICS. 



305 



be applied to remove the residual magnetism is called the coercive 
force. 

The broken curve in Fig. 180 represents a cycle of magnetization 
of a specimen of hard steel, whence it is seen that the coercive 




Fig. 180. 

force is very much greater than in the case of iron, 
already been shown in Par. 155. 



This has 



399. Energy Loss Due to Hysteresis. — In raising a weight a 
certain amount of work must be performed. If after the weight 
is raised it be released, it will in its fall restore the same amount 
of energy. In magnetizing a bar of iron or steel work is likewise 
performed but when the magnetizing force is withdrawn the entire 
amount of energy is not given back, in other words, there is a 
loss. 

In Par. 358 we saw that the work expended in changing the field 
within a coil carrying a current is IN ergs, in which I is the 
current in absolute units and AT" the increase or decrease in the num- 
ber of lines embraced. If there be n turns in the coil, the expres- 
sion becomes nIN ergs, but n being a constant the work is always 
proportional to the product of the current by the change in the 
number of lines embraced. 

In Fig. 181, AL is the average magnetizing force as the number 
of lines embraced by the coil increased from OE to OF. But we 
have seen that the magnetizing force is proportional to the 
current, therefore AL is proportional to the current and the 



306 



ELEMENTS OF ELECTRICITY. 



area of the rectangle ALxEF is proportional to IN or to the 
energy expended while the magnetization increased from OE 
to OF. In a like manner the area of the rectangle FM is pro- 
portional to the energy expended while the magnetism increased 
from OF to K. The sum of these elementary rectangles, or' the 

area SDGO, represents the total energy ex- 
~n pended in magnetizing the iron to the stage 
OG. It follows that the area FDG repre- 
sents the energy restored as the magnetiza- 
tion falls to OF, and the difference between 
these two areas represents lost energy. 
The energy lost during a complete cycle 
is proportional to the entire shaded area 
enclosed by the loop. It will be seen from 
this that the lost energy is much less in the 
case of soft iron than it is in the case of 
steel. This lost energy reveals itself in the 
form of heat, the temperature of the core 
rising. It represents waste which in the 
case of certain alternating-current ma- 
chines may assume serious proportions. It 
is largely on this account that the best and 
softest iron is used in the cores of trans- 
Fig. 181. formers (Par. 431). Ewing has shown that 
the energy consumed in subjecting one ton of soft iron to 100 
cycles of strong magnetization per second is about sixteen horse- 
power and the energy loss for a very hard tungsten steel is twenty 
times greater. 




400. Law of Magnetic Circuit. — In Par. 387 it was shown that 
the intensity of the field at the center of an indefinitely long sole- 
noid is 

H=AtNI 

in which N is the number 
of turns per centimeter and / is the current in absolute units. 
Actually it is impracticable to employ very long magnetizing coils 
but by substituting the proper values in the integral in the para- 
graph referred to, it can be shown that in applying the above 
formula to coils whose length is not less than six times their diam- 
eter, the error committed does not exceed one per cent. If the 



ELECTRO-MAGNETICS. 307 

length of the magnetizing coil be I and if the total number of turns 
be n, the above expression can be written 

H = ^ (I) 

Suppose this coil to be wrapped uniformly around an iron ring 
whose length is I and whose permeability is \x. The flux or induc- 
tion per square centimeter (the word " induction" being used in the 
sense of "crop of lines of force produced") is 

„ „ 4:TTnI.fX 
JD = Jtl/JL = 1 

If the cross-section of the core be A, the total induction is 

AirnI .A.fj. 
= 1 ' 

This may be put in the following form 

Airnl 

A fJL 

In Par. 391 it was shown that reluctance is the reciprocal of 
permeability, therefore representing 1/V by (ft, the above becomes 

* - -^- (ID 

I xft 
Ohm's law may be written (Par. 285) 

The similarity of these two expressions is striking. In the case 
of electricity, the current varies directly as the electro-motive 
force and inversely as the resistance; in the case of the magnetic 
field, the flux varies directly as the magneto-motive force and 
inversely as the reluctance. 

From (I) \rwnl, the magneto-motive force, is equal to H.l in 
which H is force in dynes and I is length in centimeters, therefore 
this magneto-motive force is measured in work, or ergs. It will be 
recalled that the electro-motive force between two points is also 
measured (Par. 72) by the work expended in moving a unit charge 
from one point to the other. 



308 



ELEMENTS OF ELECTRICITY. 



From (II) it is seen that, like resistance, the reluctance varies 
directly as the length and inversely as the cross-section of the 
magnetized body, and also as the factor (ft, which may be called 
the specific reluctance or the reluctivity of the body. It can be 
shown by the method used in Par. 288 that specific reluctance is 
measured by the reluctance of a centimeter cube of the substance. 

The foregoing analogy is not complete. The resistance of a 
conductor kept at a constant temperature does not vary with the 
current; on the other hand, the permeability, and hence the 
reluctance, does vary with the flux. 

401. Calculation of Flux. — It is seldom that the magnetic cir- 
cuit is a complete iron path as assumed in the preceding para- 
graph. It most frequently is intersected by air gaps and is 
composed of portions which differ in permeability. In such a 
case the total reluctance is the sum of the separate reluctances 
in series. As an illustration, suppose we are required to calculate 

the flux through a magnetic 
circuit as shown in Fig. 182 
consisting of an iron horseshoe- 
shaped portion M whose length 
is k, cross-section A x and per- 
meability ,ui, and a cylindrical 
iron armature B, whose average 
length is k, cross-section A 2 , 
and permeability /x 2 , the arma- 
ture being separated on either 
side from the horseshoe frame 
by an air gap of length k, cross- 




unity. 



Fig. 182. 

section 
The flux, if I be in amperes, is 

4:wnl 



A 3 and permeability 



<t> 



10 



/i 



■ lMi 



+ 



k | 2Z, 

A2/X2 A3 



As an alternative problem we may be required to calculate the 
ampere turns to produce a required flux in a given circuit. This 
involves the solution of the above equation for nl but is com- 
plicated by the decrease in permeability with increase in flux. 
The permeability under the conditions of the problem is best 
obtained from tables or from the corresponding curves of mag- 



ELECTRO-MAGNETICS. 



309 



netization (Par. 394). It may also be necessary to make allow- 
ance for a certain amount of leakage of flux which occurs at the 
air gaps. 

The foregoing calculations are not exact but they enable the 
designer of electrical machinery to approximate very closely to 
the solution of his problems. 

402. Diamagnetism. — In Par. 122 reference was made to 
diamagnetism, or the property possessed by certain bodies, 
notably bismuth, which causes them to be feebly repelled from the 
poles of a magnet. Various attempts have been made to account 
for this phenomenon, the explanation now accepted being based 
upon the theory that the permeability of these diamagnetic 
substances is less than that of the surrounding medium. Fig. 183 
represents a block of bismuth placed in a 
magnetic field. The bismuth being less per- 
meable than the surrounding air, it crowds off 
to the right and left a portion of the field. The 
tension along the lines of force causes the 
bismuth to move from the stronger into the 
weaker field, or away from the magnet. 

This hypothesis is corroborated by the fact 
that a glass tube filled with a solution of an 
iron salt is paramagnetic when suspended in 
air between the poles of an electro-magnet, but becomes diamag- 
netic when surrounded by a denser or more concentrated (and 
hence more permeable) solution of the same salt. 



; ' 1 1 M I I I I l 1 1 

// MmvvwV. 




!.'('/» 



Fig. 183. 



310 ELEMENTS OF ELECTRICITY. 



CHAPTER 32. 

ELECTRO-MAGNETS. 

403. Electro-Magnets. — The combination of a coil with a core 
of a magnetic substance, usually soft iron, which is made a magnet 
by the passage of a current through the coil is called an electro- 
magnet. The first electro-magnets were made in 1824 by the 
English scientist Sturgeon. At that time insulated wire had not 
been invented and his magnets were made by insulating the core 
by a thick coating of varnish and wrapping the wire on top of this, 
the successive turns being so spaced that they did not touch each 
other. In 1826, Joseph Henry of Albany discovered how to 
insulate wire by a silk covering. This enabled him to wrap the 
wire more closely and to put on several layers and he soon pro- 
duced electro-magnets remarkable for their power. In 1831 he 
constructed one whose iron core weighed less than sixty pounds 
yet could support over a ton. 

404. Rules for Polarity of Electro-Magnets. — After the facts 
brought out in the preceding chapters it is perhaps unnecessary 
to give a rule for determining the polarity of an electro-magnet. 
Should such be needed, the simplest is the right hand rule, which 
is merely a variation of the rule given in Par. 345. Place the 
palm of the right hand upon the coil, the fingers pointing in the 
direction of the flow of the current (Fig. 173); the extended thumb 
will point to the north pole of the magnet. Another rule frequently 
used is the following. Face the pole of the magnet; if the mag- 
netizing current flows around it in a clockwise direction it is 
a south pole; if in a counter-clockwise direction it is a north 
pole. 

405. Value of Electro -Magnets. — Electro-magnets are used 
extensively and for very varied purposes, their value depending 
upon the three following characteristics. 

(1) Their great power. They can be made very much more 
powerful than the strongest permanent magnets and they can 
also be made of much greater size. 



ELECTRO-MAGNETICS. 311 

(2) Control of magnetism. The magnetism is perfectly under 
the control of the operator and, like an electric light, may be 
turned off or on at pleasure. 

(3) Control from a distance. The control can be exerted even 
at distances of several hundred miles. 

406. Tractive Power of Magnets. — In Par. 66 it was shown 
that a unit charge placed near a plane charged to a uniform sur- 
face density 8 is acted upon by a force of 2w8 dynes. A frequently 
employed conception of magnetism is that the intensity of 
magnetization is due to the number of unit poles spread over the 
polar or terminal surface of the magnet (Par. 133). If N (Fig. 
184) be the pole of a bar magnet and if S be a bar of soft iron or 
other magnetic substance placed so near N that all the lines of 
force which emerge from N enter S, then there will be as many 




unit poles upon £ as there are upon N. The force between N 
and S will be one of attraction. If we consider that the magnetism 
upon N is uniformly distributed and equivalent to 8 unit poles 
per square centimeter, then the same course of deduction as 
followed in Par. 66 will show that a unit pole at P is attracted 
with a force of 2t8 dynes. If the sectional area of N he A, there 
are upon N, A8 unit poles. There are an equal number upon S, 
each of which is acted upon by a force of 2t8 dynes, therefore, 
the total attraction between N and S is 

F=2ir8XA8=2ir.A.8 2 dynes (I) 

Since from each unit pole there radiate 47r lines of force (Par. 
145), the total number per square centimeter between iV and S 
is H = 4:7r8, whence 8 = H/At. 

Substituting in (I) above we have 

H 2 

or the tractive force 
exerted by a magnet is proportional to the square of the number of 
lines of force per square centimeter of pole surface. 



312 ELEMENTS OF ELECTRICITY. 

Ewing states that by using very high magnetizing iorce a 
magnetic pull of over 225 pounds per square inch has been 
obtained. 

A curious consequence follows from the above. By decreasing 
the pole area we increase the tractive power of the magnet. This 
is because as we decrease the area we increase the number of lines 
of force per square centimeter and the tractive power varies as 
the square of this number. This is the explanation of the fact 
referred to in Par. 124, namely, that if one end of a bar magnet 
be square and the other end be rounded, the rounded end will 
exert the greater pull. The powerful electro-magnets used in 
hospitals to extract particles of iron from the eye have long 
conical poles. 

The above expression for the tractive power seems to indicate 
that this power is independent of the distance between the pole 
and the body, but actually the force does fall off very rapidly as 
we recede from the pole. The explanation is that as we increase 
the air gap we increase very greatly the reluctance of the magnetic 
circuit and this in turn decreases the flux or H. (Par. 401.) 

407. Shape of Electro -Magnets. — Since the pull of a magnet 
varies as the square of the flux per square centimeter and since 
this flux varies inversely as the reluctance of the magnetic circuit, 
electro-magnets, as a rule, are designed so that the air gaps in the 
circuit are as small as possible. The majority therefore are either 
of the horseshoe pattern or bent to three sides of a rectangle. 
The magnetizing coil may be wrapped over the whole length of 
the horseshoe, or only on the central part or yoke, but most 
frequently two coils are used, one being wrapped on each leg of 
the core. In small instruments these coils are called spools or 
bobbins. The dimensions and relative proportions of the parts of 
these magnets are varied according to the use to which they are 
to be put. 

408. Use of Electro- Magnets. — The uses to which electro- 
magnets are put may be classed under two general heads; (a) for 
creating the magnetic fields required for the operation of certain 
electrical machines and (b) for exerting a tractive effort or pull. 
The use for creating fields will be described when the subject of 
electrical machinery is reached. The second heading embraces 
a most varied class of uses among which are (1) lifting weights, 



ELECTRO-MAGNETICS. 



313 



(2) operating annunciators, call and alarm bells, etc., (3) tel- 
egraphy, (4) operating automatic switches, (5) regulating the 
feed of the carbons of an arc light, regulating clocks from a master 
clock, etc. Only a few of these can be described. 

409. Lifting Weights by Electro -Magnets. — Electro-magnets 
are largely used in handling scrap iron, steel billets, boiler plates, 
etc. The magnet employed is shown in section in Fig. 185. The 
core is a short and heavy one- 
piece casting consisting of an 
inner cylindrical core sur- 
rounded by an annular space 
in which the magnetizing coil 
is wound, the whole being called 
an iron-clad electro-magnet. 
When the current is turned on, 
the inner core becomes one 
pole and the outer ring the 
other. Owing to the large 
cross-section and little length 
of the iron and to the shortness 
of the air gap when a piece of Fig. 185. 

iron is in contact with the poles, the pull is very powerful. This 
magnet, suspended from a derrick, is lowered upon the pile of 
scrap iron that is to be moved, the current is turned on, the magnet 
with the clinging mass of iron raised, swung over to where it may 
be desired, the current turned off and the iron dropped. In 
handling such objects as boiler plate, it avoids the necessity of 
using and adjusting hooks, chains or ropes. The coil is thoroughly 
protected from accidental injury, a sheet of brass usually being 
inserted in the annular space. 

410. Electric Bells. — A common form of electric bell is shown 
diagrammatically in Fig. 186. It consists of the bell or gong G, 
the hammer H, the electro-magnet M, the battery C (usually 
one or two dry cells), and the push button D. The hammer is a 
metal knob on a slender arm pivoted at P and bearing at its 
middle the soft iron armature A. A delicate spiral spring S is 
attached to the arm and exerts upon it a pull from the magnet. 
At the back of the armature there is a slender brass strip which 
makes contact at B with an adjustable screw. When the button 




314 



ELEMENTS OF ELECTRICITY. 



D is pressed, closing the circuit, a current flows from C to D, 
thence to B, thence to P, thence through the coils of M and back 
to C. The cores of M are magnetized by this current, attract the 
armature A, causing the hammer to strike the bell, but at the same 
time break the circuit at B. The circuit being broken, M is no 
longer magnetized, the spring S pulls the armature back to its 




r 1 




Fig. 186. 

original position, and the contact at B is restored. This causes the 
hammer to strike the bell again and so on, a rapid succession of 
blows being given so long as the button is pressed. Arrangements 
of this kind for rapidly making and breaking a circuit are called 
interrupters. 

411. The Electric Telegraph. — The word "telegraph" meant 
originally to convey messages by exchanging signals at a distance. 
During the wars of Napoleon there was developed a system of 
semaphore signals by which messages could be transmitted 
rapidly from point to point. We read in the contemporary 
accounts of the campaign in the Spanish peninsula that Napoleon 
telegraphed his instructions from Paris to his corps commanders 
in the field. 

The sending of signals by means of electricity was tried by 
many. An insulated wire between two points was given a static 
charge which caused a pith ball at the far end of the wire to stand 
out. If a charged body be moved near the other end of the wire 
corresponding movements could be produced in the pith ball. 



ELECTRO-MAGNETICS. 



315 



Sparks from a Ley den jar were transmitted over a wire in ac- 
cordance with a prearranged code. Use was made of the electro- 
lytic effect of a current. Twenty-six separate wires, each marked 
to correspond to a certain letter of the alphabet, were stretched 
between two points and at the receiving station the ends of these 
wires dipped into an acidulated solution. A single wire led from 
the solution to the ground. At the sending end a voltaic pile was 
used, one pole of which was "grounded." When the other pole 
was touched to one of the twenty -six wires, the circuit was com- 
plete and bubbles of gas appeared at the corresponding end at 
the receiving station. These various methods failed mainly 
because of the lack of a steady source of electricity. This difficulty 
was overcome by the invention in 1836 of the Daniell cell. In 
the following year Congress was induced to make an appro- 
priation of $30,000 for the erection between Baltimore and 
Washington of a line to test the system invented by Morse. This 
proved successful and with minor variations is in operation to-day 
over the greater part of the globe. It is estimated that there are 
now over five million miles of land telegraph lines in use. 

412. The Morse Telegraph. — The principle of the Morse 
telegraph will be readily understood from the following. In the 
diagram (Fig. 187) K is the sending and M the receiving station. 



D 



M 







77777777jty//////////^ 



Fig. 187. 

R is a roll of paper ribbon which is slowly unwound by clockwork 
in the direction shown by the arrow. B is a battery of Daniell 
cells, one pole of which is grounded at E. When the key K is 
closed the current travels from the battery over the line to the 
electro-magnet M, thence to the ground at E\ thence back 
through the earth to E. When M becomes magnetized, the iron 
armature A is pulled down. This causes the end P of the lever 
to rise and to press a pencil against the moving ribbon at D. 
When the key K is opened, the circuit is broken and a little 



316 



ELEMENTS OF ELECTRICITY. 



spring S pulls the pencil away from the ribbon. The length of 
the pencil mark on the ribbon varies therefore with the length of 
time that K is kept closed and the Morse alphabet is accordingly 
made up of a system of dots, dashes and intervals or spaces. If 
there be in the face of the drum D a groove, and if P instead of 
being a pencil is a hard and smooth stylus which presses above 
this groove, there will be produced in the ribbon long and short 
indentations. 

While the foregoing gives the principle of the Morse telegraph, 
in actual practice certain conditions arise which cause a consider- 
able modification in the simple arrangement described above. 
These are the following: 

(1) Each station must be able both to send and to receive. 

(2) The line must be so arranged that intermediate stations 
may be operated. 

(3) If the key K, Fig. 187, be left open, the circuit is broken 
and it would be impossible for an operator at M to send a signal 
to K. Accordingly, in the American system the key K is kept 
closed when not in use, in other words, there is a current constantly 
flowing over the line. This would appear to be a wasteful method 
and is avoided in the European system, but actually the current 
(and the consequent waste) is very small, and since the European 
system requires a greater number of batteries, the cost is about 
the same. 

^3 




Fig. 188. 

(4) It was soon discovered that the signals could be read by 
ear and therefore the recording apparatus is now generally 



ELECTRO-MAGNETICS. 



317 



omitted and in its place is substituted a sounder, an instrument 
shown in simplest form in Fig. 188. A horizontal brass lever L, 
pivoted at P, is pulled down at one end by the spring S until the 
other end is pressed up against the adjustable contact B. The 
lever carries on its upper side the crosswise soft iron armature A 
and below this armature is the electro-magnet M. When a current 
flows through M the core is magnetized, A is attracted and the 
lever is pulled down until the contact D strikes the brass frame 
just below, making a loud click. When the current is broken the 
spring S causes the lever to fly up and strike B, making a second 
click. The interval between these successive clicks determines 
whether the sound be a dot or a dash. 

(5) The currents employed are only a few thousandths of an 
ampere (not entirely through choice but because of the resistance 




Fig. 189. 



of the line), and are usually not strong enough to actuate directly 
either the recording device or the sounder. Morse overcame this 
difficulty by means of a relay, an electro-magnet so placed in the 
main circuit that when a current flowed the magnet attracted 
an armature which in its movement closed an auxiliary circuit, 
thereby throwing in a local battery which supplied the necessary 
current to operate the recording apparatus. This arrangement 
is shown diagrammatically in Fig. 189 in which M is the electro- 
magnet in the main line LL, A is the armature, hinged at P and 
drawn up against the adjustable stop K by the feeble tension of 
the spring S. When a current passes through M, the armature A 



318 



ELEMENTS OF ELECTRICITY. 



is attracted and makes contact at C, thus throwing in on the 
sounder the auxiliary battery B. The armature is therefore 
really a switch or key for the local circuit. 

413. The American System. — The operation of the American 
system will be understood from Fig. 190. The operator in Boston, 
preparatory to signalling, opens the switch S of his sender. This 




W///////////////////////////////^^^ 



Fig. 190. 

breaks the circuit and stops the current in the line. When he 
closes his key K, the circuit is restored, a current flows, each of 
the electro-magnets pulls down its relay armature thus causing 
every sounder to click. A signal made at one station is therefore 
repeated at every station on the line. Should the New York 
operator wish to interrupt, he opens his switch S, thus break- 
ing the circuit. The Boston operator is aware of this at once 
because his own sounder ceases to click, and he at once closes 
his switch and awaits instructions from New York. Whenever 
a message is completed, the operator must at once close his 
switch. 

Should a break occur in a line, it is still possible to use the 
remainder. Thus, should a break occur between Providence and 
Boston, the Providence operator by grounding his line, as shown 
by the dotted line, restores communication with New York. 
Should the break be between Providence and New York, he must 
ground his line to the right of his key. 



ELECTRO-MAGNETICS. 



319 



414. Overload Switch. — Should a short circuit occur on an 
electric- lighting or on a power circuit, serious injury may result. 
Various automatic devices are employed to afford protection in 
such cases. We saw in Par. 306 the use of fuses for this purpose. 
There have been devised many kinds of switches which auto- 
matically break the circuit when the current exceeds a certain 
maximum for which they are set. These are called circuit-breakers 
or overload switches, the word "load" in electric parlance meaning 
current. They are therefore analogous to safety valves. 

One of these is shown diagrammatically in Fig. 191. The 
switch A when closed makes 
contact through a curved arm 
with two points B and C. A 
stout spring, S, tends to throw 
the switch in the direction 
shown by the arrow but is 
prevented from doing so by a 
hook H which engages in a 
corresponding hook on the trig- 
ger T. The current enters at 
E, passes thence to B, thence 
through the switch to C, thence 
around the coil G and out by F. 
Within the coil G there is a 
soft iron core. As the current 
increases in strength, the coil 
exerts a greater and greater 
pull upon this core until finally 
it is lifted bodily. As it moves 
upward it strikes the trigger T, 
releasing the switch which is 
then thrown forcibly up, thus 
breaking the circuit. The Fig. 191. 

farther the core is inserted in the coil, the more easily it is lifted, 
therefore, by means of the screw K, the switch may be set to trip 
at any desired limit. 

415. Underload Switch. — Automatic switches are also in use 
which trip when the current falls below a certain minimum. One 
form is shown diagrammatically in Fig. 192. An arm, pivoted at 
P, carries at one end a weight W and at the other end an arc of 




320 



ELEMENTS OF ELECTRICITY. 



wire whose extremities dip into mercury cups. The current, flow- 
ing as shown, passes around M, thence to the first mercury cup, 
thence across the arc to the second cup and out. The armature A 
is attracted and held by the electro-magnet M. When the current 
decreases below a certain point, M can no longer hold A, the 
weight W falls and lifts the ends of the arc out of the mercury 

cups, thus break- 
ing the circuit. 
Instead of these 
"mercury break" 
switches, prefer- 
ence is now given 
to forms similar 
to the overload 
switch, described 
in the preceding 
paragraph, the switch being thrown open by a compressed spring 
when the current falls below a certain minimum. 

At first sight it is not clear why an underload switch is needed. 
The following is an example of its use. Fig. 193 represents a 
storage battery B being charged by current from a generator G 
through an underload switch S. It was shown in Par. 245 that 
in order to drive a current through the battery, the E. M. F. of 
the generator should be about ten per cent greater than that of 
the battery. Suppose that by some accident during the charging, 




t 



iiii "--iiiiih^s; 



Fig. 193. 

such as the belt slipping, the generator should slow down or 
should stop. The moment the E. M. F. of the generator falls 
below that of the battery, the battery would at once begin to 
discharge back, and the resistance of the generator being very 
small, the discharge would amount to a short circuit. However, 
before a current can be reversed it must die down and pass through 
zero, therefore, before the battery could discharge, the underload 
switch would trip and thus protect it. 



ELECTRO-MAGNETICS. 



321 



CHAPTER 33. 

INDUCTION. 

416. Faraday's Discovery of Induction. — In Fig. 194, C is a 

hollow cylindrical coil of wire connected in circuit with a galva- 
nometer G, and M is a magnet held above the coil. If the magnet 




A 




if^CZ^ 




Fig. 194. 

be quickly thrust into the coil, the galvanometer needle will be 
deflected indicating a current in C, but the deflection is only 
momentary and if the magnet after insertion be held motionless, 
the needle will at once return to its zero position. If, after the 
needle has come to rest, the magnet be quickly withdrawn from 
the coil, the galvanometer will again indicate a momentary 
current but in this case in a direction opposite to that produced by 
the insertion of the magnet. The more rapidly the magnet is 
inserted or withdrawn, the greater the momentary current as 
indicated by the greater deflection of the galvanometer needle. 
If the magnet be reversed end for end, the currents will likewise 
be reversed. Finally, if the magnet be held motionless and the 



322 



ELEMENTS OF ELECTRICITY. 



coil be moved, the same results are obtained, that is, the motion 
of the magnet and coil need only be relative. 

These facts were discovered by Faraday in 1831. Their 
importance can hardly be overestimated since they are the basis 
of nine- tenths of the present commercial production of electricity. 
The currents produced in the coil by these movements are said 
to be induced and the phenomenon is called induction. 

If there be a break in the circuit of the coil there will be an 
induced E. M. F. but no current, and, to avoid repetition, it is 
to be borne in mind hereafter that whenever reference is made to 
induced E. M. F. there will also be an induced current in the same 
direction, provided the circuit be complete. 

We have already seen (Par. 403) how a magnet may be pro- 
duced by the electric current; the above shows the reverse proc- 
ess, the production of an electric current by means of a magnet. 
It must, however, be noted that in the production of a magnet by 
means of a current there is an expenditure of electrical energy, 
while in the production of a current by means of a magnet there 
is no loss of magnetism and the magnet suffers no diminution in 
strength. More physical energy is required to move the magnet 
or the coil relative to each other than is required if a soft iron 
bar of equal weight be substituted for the magnet, and this extra 
energy is the source of the electrical energy. 

417. Faraday's Second Discovery. — Since inserting into the 
coil an unmagnetized bar of iron or steel, otherwise exactly similar 




Fig. 195 



to the magnet, produces no effect, it follows that the current must 
have been produced, not by the movement of the magnet alone 
but by the movement of the field surrounding the magnet. Since 
this field consists of space traversed by lines of force, we may state 
that if lines of force are thrust into or withdrawn from a circuit, 
an E. M. F. is induced in the circuit. It is not necessary that the 



ELECTRO-MAGNETICS. 323 

magnet be actually inserted in the coil provided it be so moved as 
to alter the number of lines of force traversing the coil. It follows 
logically from the foregoing that induced currents may be pro- 
duced by using lines of force produced otherwise than by magnets, 
that is, by currents. 

In Fig. 195 B represents a battery, P a coil of wire and S a 
second coil near to the first and connected to the galvanometer G. 
There is no electrical connection between P and S. With K 
closed and a current flowing in P, the galvanometer will indicate 
a momentary induced current in S if P be moved nearer to S, and 
a momentary current in the opposite direction if P be moved 
farther from S. This production of an induced current by vary- 
ing the position of a current with reference to a circuit was the 
second of Faraday's discoveries in induction. To the coil P he 
applied the name primary, and to the coil S, the one in which the 
current is induced, the name secondary. 

Without varying the position of P and S, a momentary current 
is induced in S whenever K is closed, and one in the opposite 
direction when K is opened. These are but extreme cases of the 
general case above, for to close the key is equivalent to bringing 
up a current to P from an infinite distance, and to open the 
key is equivalent to removing the current in P to an infinite 
distance. 

In the case of the magnet, induction took place only while the 
magnet was moving; so in this case induction takes place only 
while the current in the primary is changing, or while the primary 
with current flowing is being shifted in position relative to the 
secondary. 

418. Inertia of Electro -Magnetic Fields. — A physical explana- 
tion of induction may be given if the following preliminary con- 
ceptions be grasped. 

(a) The space embraced by an electric circuit is at any given 
time pervaded by n lines of force. If the convention be adopted 
that lines in one direction are positive, then those in the opposite 
direction must be considered negative and therefore n may have 
any value, positive, or negative, or zero. 

(b) Positive and negative lines of force neutralize each other, in 
other words, a sufficient number of lines of force of one kind may 
be introduced into a field of the opposite kind to weaken the field, 
or to reduce it to zero, or to reverse it. 



324 



ELEMENTS OF ELECTRICITY. 



(c) Electro-magnetic fields possess a property which has been 
termed electro-magnetic inertia and which is analogous to the 
inertia of matter. Inertia is a property of matter by which the 
matter resists any change of its state with respect to rest or motion. 
Thus, a body at rest resists being put in motion and a body in 
motion resists being accelerated, retarded, turned aside, or stop- 
ped. This resistance manifests itself only so long as the change 
in the state of the body is being made and disappears the instant 
the change is accomplished. Electro-magnetic inertia may be 
said to be the property by which electro-magnetic fields resist any 
change in the number or direction of their lines of force. This 
resistance manifests itself as E. M. F. and corresponding current 
in the circuit, which current tends to produce lines of force of such 
number and kind as to keep the original number constant. Like 
the inertia of mass, it reveals itself only while the change in the 
number of lines in the field is taking place and vanishes as soon 
as the change has taken place. 

419. Explanation Applied to Magnet and Coil. — To illustrate, 
consider the case of the magnet and the hollow coil (Fig. 196). 




At the outset, the number of lines in the field of the coil may be 
considered zero. If we thrust in the magnet in the direction shown 
in the figure, we push in lines of force from above downward. 



ELECTRO-MAGNETICS. 



325 



The current induced in the coil is in such direction as to produce 
lines of force upward, that is, tending to neutralize those which 
are being inserted and thus keeping the original number in the 
field unvaried. Applying the right hand rule (Par. 404), we see 
that, looking down into the coil from above, the induced current 
will be counter-clockwise. 

Had the magnet been reversed and the south pole been inserted 
in the coil, the lines of force would have been thrust in in a nega- 
tive direction, or pointing upwards, which must be considered as a 
decrease in the number in the original field. The induced current 
would therefore have been in such direction as to send lines of 
force downward, that is, viewed from above, it must have been 
clockwise. 

Upon withdrawing the magnet in the first case, we decrease the 
number of lines embraced by the coil. The induced current is in 
such direction as to compensate for this withdrawal by producing 
lines running downward, hence, looking at the coil from above, 
the current is clockwise. 

Similarly, withdrawing the magnet which had been inserted 
south end foremost produces a counter-clockwise induced current. 

420. Explanation Applied to Two Coils. — Consider the case of 
the two coils as described in Par. 417. Upon closing the key (Fig. 
197) the current flows around P as indicated. This produces in 



■tl 


s 

^3- 


/Ci — 




197 



the coil P lines of force in the direction shown by the large arrow, 
and as the two coils are now placed, some of these lines pass 
through S thus changing the number of lines in the latter 's field. 
The current induced in S is in such direction as to produce lines of 
force opposed to those coming from P. This current, viewed from 
P, is therefore counter-clockwise. 

Similarly, when K is opened the effect is to withdraw these 
lines of force from S and the current induced in S is in direction tc 



326 



ELEMENTS OF ELECTRICITY. 



produce others to replace those being withdrawn, hence, seen from 
P, the current is clockwise. 

With the current flowing in P, changes in the position of P with 
respect to S vary the number of lines through S and induce cur- 
rents in S in accordance with the principles just given. 

421. Rule for Direction of Induced E. M. F. — A simple rule for 
remembering the direction of the induced E. M. F. (and current) 
in a coil is the following. Look through the coil in the positive direc- 
tion of the lines of force; a decrease in the number enclosed induces a 
clockwise E. M. F.; an increase induces a counter-clockwise E. M. F. 

422. Right Hand Rule for Direction of Induced E. M. F.— There 
are certain cases where the beginner may be perplexed as to the 
application of the foregoing rule. Thus, the conductor under 




consideration may not form a coil but may be a straight piece of 
wire, or there may be a coil but its position may be in doubt, only 
a portion of it being visible. For example, the coils on the arma- 
ture of a dynamo are often interwoven in an intricate manner and 
further concealed by a covering of insulating material, yet it may 
be necessary to determine the direction of the induced E. M. F. 



ELECTRO-MAGNETICS. 



327 



In such cases the following right hand rule seems to be the sim- 
plest. Place the right hand upon the conductor, the thumb point- 
ing in the direction of its motion, the palm turned to receive the lines 
of force of the field; the extended fingers will indicate the direction of 
the induced E. M. F. 

In Fig. 198 the conductor AB is moving upward and the direc- 
tion of the induced E. M. F. is from A to B. 




These two rules are of course perfectly compatible. For ex- 
ample, suppose AB (Fig. 199) to be a part of either the coil ABC 
or of the coil ABD. If it be ABC, the upward movement will 
carry it out of the field, there will be a decrease in the number of 
lines embraced and the induced E. M. F. will be clockwise, or from 
A to B. If it be A BD, the upward movement will carry it into 
the field, there will be an increase in the number of lines embraced 
and the induced E. M. F. will be counter-clockwise, or again from 
A to B. 

If the plane of the coil be moved parallel to the lines of force. 
or if the coil be moved parallel to itself in a uniform field, there is 
no increase or decrease in the number of lines embraced and con- 
sequently no induced E. M. F. This same conclusion may be 



328 ELEMENTS OF ELECTRICITY. 

derived from Par. 358. To induce E. M. F. there must be an ex- 
penditure of energy, but since the number of lines embraced by 
the coil is unaltered, there is no such expenditure. From another 
point of view it may be considered that in each half of the coil 
there is induced an equal E. M. F. but these being in opposite 
directions, the resultant E. M. F. is zero. 

423. Mechanical Production of Electric Current. — Since the 
insertion of a magnet into a coil induces a momentary current and 
the withdrawal of the magnet induces a momentary current in 
the opposite direction, it is possible to construct a machine by 
which a reciprocating motion is given to a magnet which alter- 
nately enters and recedes from a coil and thus induces an alternat- 
ing current in the coil and in its circuit. Such a machine would be 
of low efficiency. But we have also seen (Par. 417) that it is not 
necessary to actually insert the magnet into the coil provided it 
be so moved as to vary the number of lines of force through the 
coil. For example, it could be swept across the mouth of the coil. 
This is the basis of the construction of modern machines for gen- 
erating electric current. A number of coils are fixed radially upon 
the outer circumference of a circle which rotates within a larger 
circle upon whose inner circumference are attached magnets, or 
they may interchange places and the magnets may rotate and the 
coils remain fixed. As the coils and the magnets sweep by each 
other at high speed, alternating currents are induced in the coils 
and are drawn off and utilized. Such machines are called gener- 
ators and are explained in detail later on. (See Fig. 337.) 

424- Cutting Lines of Force. — Electro-motive force is induced 
by varying the number of lines of force embraced by a circuit. A 
line of force is a closed curve. A circuit is also a closed figure. 
Therefore, like two links of a chain, in order that a line of force 
may be inserted into or withdrawn from a circuit, one or the other 
must be cut and it is usually the line of force. Hence, on account 
of the conciseness of the expression, it is convenient and custom- 
ary to speak of the E. M. F. generated by "cutting lines of force.' ' 
It must, however, be remembered that, as was shown in Par. 422, 
in speaking thus we mean by the number cut the number by which 
the original field embraced by the circuit has been increased or 
decreased, for when a circuit is moved parallel to itself across a 
uniform field, there are certainly lines cut, but since the original 
number embraced is unvaried, there is no E. M. F. induced. 



ELECTRO-MAGNETICS. 



329 



425. Relation Between Rate of Cutting of Lines of Force and 
the Resulting E. M. F. — In Par. 416 it was shown that the more 
rapidly the field embraced by the coil is varied, the greater is the 
induced E. M. F. The relation between the induced E. M. F. and 
the rate of cutting of lines of force may be deduced as follows. 




Fig. 200. 

Let EG and DF, Fig. 200, represent two parallel metal rails con- 
nected across DE and embracing between them a uniform field 
whose positive direction is upward. Let AS be a wire resting 
across these rails. If this wire be slid along towards DE, there 
will be induced a current / which will flow around the enclosed 
rectangle in the direction ABED. If the movement of the wire 
and the resulting flow of current continue for a time dt, the total 
quantity of electricity which is moved around the circuit is 
Q = I.dt, whence / =Q/dt. If during this time the number of lines 
of force embraced by the rectangle be decreased by d N, the work 
done (which has resulted in moving these Q units around the cir- 
cuit) is (Par. 358) W = I.dN. 

Substituting in this the expression for / above, we have 

dN 



W=Q 



dt 



The E. M. F. induced in the circuit being E, if the circuit be cut 
at any point there will be a difference of potential E between the 
opposite sides of the resulting gap. In Par. 72 it was shown that 
the difference of potential between two points is measured by the 
work expended in moving a unit quantity of electricity from one 
point to the other. Since, from the above, it required an expendi- 
ture of Q . d N /dt ergs to move Q units through this difference of 
potential, to move one unit requires d N /dt ergs, hence 



E 



dN 
dt 



or the induced E. M. F. varies 
directly with the rate of cutting of the lines of force. 



330 ELEMENTS OF ELECTRICITY. 

Had the coil consisted of n turns, the work done would have been 
W=Q.n.dN/dt (Par. 358) and hence 

or the induced E. M. F. also 
varies directly with the number of turns in the coil. 

It is a simple matter to confirm experimentally the foregoing 
conclusions. 

426. Absolute Electro-Magnetic Unit of E. M. F.— If a coil 
embraces N' lines of force and after an interval t embraces N", 
the average E. M. F. generated is 

N'-N" 
E = — 

If N' — N" be positive, there has been a decrease in the number 
of lines embraced and the induced E. M. F. is positive or clockwise. 
If it be negative, the induced E. M. F. is negative or counter-clock- 
wise. 

If in the above expression N f — N" be unity and t be one 
second, E becomes unity, whence the absolute electro-magnetic 
unit of E. M. F. is defined as that E. M. F. induced by cutting one 
line of force per second. 

427. The Practical Unit of E. M. F., the Volt.— The absolute 
unit of E. M. F. is entirely too small for practical purposes, and 
even a unit corresponding to the E. M. F. produced by the cutting 
of one million lines per second is extremely small. In deciding 
upon a practical unit, the Paris Congress of Electricians in 1881 
might have taken the E. M. F. produced by cutting one million, 
or ten million, or one hundred million, or even one billion lines of 
force per second, but in this selection they were probably guided 
by the following considerations. Before the adoption of a unit of 

E. M. F., the need for such a unit had been felt and it was quite the 
custom to take as an every-day standard of comparison the E. M. 

F. of a Daniell cell, the most constant cell then in general use. 
In the older books we frequently find E. M. F. specified in terms 
of that of so many Daniell cells. To disturb these conceptions 
as little as possible, the practical unit was selected as that one 
which most nearly approximated to the E. M. F. of a Daniell 
cell. The practical unit of electro-motive force, the volt, is there- 



ELECTRO-MAGNETICS. 



331 



fore defined as the E. M. F. produced by cutting one hundred million 
(10 8 ) lines of force per second. The volt is therefore equal to 10 8 
absolute units of E. M. F. The average E. M. F. of a Daniell 
cell is 1.07 volt (Par. 206). 

If in Ohm's law, I = E/R, we substitute for I its value in 
absolute units Ixl0~ l , and for E its value Z?Xl0 8 , we see that 
for R we must put R X 10 9 , therefore, the ohm is 10 9 absolute units 
of resistance. 

428. Eddy Currents. — In the preceding paragraphs we have 
considered currents induced in coils when the flux embraced by 
the coils is varied. The phenomenon of induction is still more 
general and whatever the shape of a conductor, that is, whether it 
be a sphere, or a plate, or an irregular lump, currents are induced 
in it whenever there is an increase or decrease in the number of 
lines of force penetrating the body. 

In 1824 Gambey observed that a compass needle set to oscillat- 
ing above a sheet of copper came to rest much more quickly than 
when placed above a wooden board. This observation was in- 
vestigated by Arago who made the additional discovery that a 
disc of copper rotated either above or below a needle produces a 
deflection of the needle in the direction of the rotation, and if 
rotated rapidly enough would cause the needle also to take up a 
motion of rotation. This experiment is noteworthy since the 
endeavor to account for the movement of the needle led Faraday 
to the discovery of induction as outlined in paragraphs 416 and 
417 above. 




Fig. 201. 

The movement of the needle may be explained as follows: NS, 
Fig. 201, represents a needle suspended above a copper disc which 
latter is caused to rotate in a clockwise direction. Consider at 
any one instant a strip AB along the diameter of the disc and 



332 ELEMENTS OF ELECTRICITY. 

parallel to the needle above. The lines of force from the north end 
of the needle radiating in all directions, some of them penetrate 
the disc. The strip A B is therefore a conductor moving across a 
magnetic field and application to each half of A B of the right 
hand rule for direction of induced currents (Par. 422) shows that 
a current flows from B to A, returning by the right and left as 
shown by the broken lines. But, such a current will, in accord- 
ance with Oerstedt's rule (Par. 345), cause the north pole of the 
needle to move off in a clockwise direction. 

Such induced currents flowing around through the mass of the 
conductor and returning upon themselves, are, from analogy with 
the circular whirls produced in running streams, called eddy 
currents. 

Reflection will show that if the copper plate in the above experi- 
ment be suspended by a thread and the needle be rotated just 
below it, the plate will take up a motion of rotation in the same 
direction. On account of the feebleness of the needle, it is custom- 
ary, in showing this fact experimentally, to employ an electro- 
magnet. The principle involved in these experiments is applied 
in the induction motor, a machine to be described later. 

429. Foucault's Experiments. — Foucault arranged a copper disc 
to rotate like a circular saw between the poles of an electro-magnet. 
When the current was off, the only energy required to rotate the 
disc was that to overcome the friction of its bearings, but as soon 
as the cores were magnetized, resistance to the turning was experi- 
enced. If, in spite of the resistance, the disc was forced to rotate, 
it rapidly grew hot. Foucault showed that this heating was due 
to the circulation of the eddy currents in the copper. If narrow 
radial slits were sawed in the disc, thus interrupting the paths of 
these circular currents, the resistance to turning and the accom- 
panying heating effect disappeared. On account of these experi- 
ments, eddy currents are often spoken of as Foucault's currents, 
but the two names are synonymous. 

In order to produce an electric current there must be an expendi- 
ture of energy. This heating effect therefore represents waste 
energy and is of much importance in any electrical apparatus in 
which the flux is frequently varied, such as electro-magnets, 
transformers and electric generators and motors, especially those 
employing alternating currents. To avoid this loss of energy, 
and also to avoid excessive heating, the cores of electro-magnets 



ELECTRO-MAGNETICS. 



333 



are sometimes made of bundles of soft-iron wires, and the cores of 
transformers and of the field magnets and armatures of electric 
machines are laminated, or built up of many thin sheets of soft 
iron, the principle being that since the eddy currents flow in closed 
curves whose planes are perpendicular to the lines of force of the 
core, they may be checked if the cores be split up by planes parallel 
to the lines of force. 

430. Lenz's Law. — If a copper cylinder be suspended by a thread 
so as to hang between the poles of an electro-magnet, and if this 
thread be twisted and then released, the cylinder by its weight 
will cause the thread to untwist and, if the current be turned 
off, will rotate rapidly. If now the current be turned on, the 
rotation will be instantly checked as if an invisible brake had 
been applied. 

The principle involved in this phenomenon was given by Lenz 
in the form of a general law to the effect that the currents induced 
by moving a conductor in a magnetic field are of such direction that 
their reaction tends to stop the movement which produces them. 

The following illustration will make this clear. Fig. 202 repre- 
sents the same arrangement of two rails and a sliding wire as ex- 




Fig. 202. 

plained in Par. 425. If AS be pushed in the direction F, a current 
will be induced flowing from A to B (Par. 422). A B is therefore 
a conductor carrying a current and placed in a magnetic field. 
By Par. 352 it is acted upon by a force in the direction R, that is, 
diametrically opposed to F. 

The foregoing affords the correct explanation for the electrical 
damping referred to in Par. 379. 

431. Transformers. — It was shown in Par. 425 that the E. M. F. 
induced in a coil varies with the number of lines of force introduced 
or withdrawn in a given time. The flux produced within a coil 
varies with the permeability of the core. If a coil be wrapped 



334 



ELEMENTS OF ELECTRICITY. 



upon a soft iron core, a current flowing through this coil will pro- 
duce many more lines of force within the coil than would be 
produced if the inner core were absent. The inductive effect is, 
therefore, very greatly increased by inserting in the coil an iron 
core. 




Fig. 203. 



Fig. 203 represents an iron rod upon which is wrapped the 
primary coil and on top of this the secondary. It will be seen that 
any lines of force produced in the primary must of necessity be 
embraced by the secondary. The following consideration will 
show that this arrangement may be still further improved. The 
lines of force which emerge from one end of the iron core must 
pass through the air to enter the other end. This long air-gap in 
the magnetic circuit very materially reduces the total flux (Par. 
401). It is therefore better to bend the iron rod into a ring, or 
similar closed figure, so that the entire paths of the lines of force 
will lie in iron. 




Fig. 204. 

Faraday devised the arrangement shown in Fig. 204, a soft iron 
ring A, on one side of which is wrapped the primary P, and on 
the other side the secondary S. When a current / is sent through 
P as indicated, clockwise lines of force are produced in the iron 
core A. When these lines penetrate S, a current V is induced, its 



ELECTRO-MAGNETICS. 335 

direction being as shown. If the current I produces N lines of 
force and if there are n turns in P, the work done in P is InN 
ergs (Par. 358). If there are n' turns in S, the work done as these 
N lines penetrate S is I'n'N ergs. The work in the two coils 
being equal, 

InN = I'n'N 

and since in each coil this work is done in the time t, we may write 

In l = In T 

But (Par. 425) nN/t is the E. M. F. in the primary and n' N/t 
is that in the secondary. Representing these by E and E' respec- 
tively 

IE = I'E' 

or I:F=E':E 

that is, the currents are to each other inversely as the number of 
turns in the respective coils; the voltages are to each other directly 
as the number of these turns. In the secondary coil, the current 
and voltage vary reciprocally, that is, as one increases, the other 
decreases so that their product is constant. Should there be ten 
times more turns in the secondary than in the primary, the in- 
duced current in the secondary will be only one- tenth of that in 
the primary, but its voltage will be ten times greater. 

Since either coil may be used as the primary, the other one being 
the secondary, it is possible with this arrangement to trans- 
form at will a changing current (i. e., one which is increasing or 
decreasing) into another whose voltage is either higher or lower 
than that of the original current. For this reason it is called 
a transformer, this particular one being known as Faraday's 
ring transformer. Those which increase the voltage are called 
step up transformers; those which lower it are called step down 
transformers. 

The assumption above that the work in the secondary is equal 
to that in the primary is not strictly correct. There is always 
some magnetic leakage and some of the lines produced in the 
primary do not penetrate the secondary. Again, a part of the 
energy of the primary is wasted in producing eddy currents in 
the core and another portion in overcoming hysteresis (Par. 399") . 
This waste, however, is reduced to a minimum by constructing 



336 



ELEMENTS OF ELECTRICITY. 



the core of thin punchings of soft iron of the shape shown in Fig. 
205. This lamination of the core avoids eddy current losses (Par. 
429) ; and the two coils being wrapped one above the other around 
the central portion and the magnetic circuit being complete to 
the right and left, the leakage is very small. In the best modern 
transformers, the total loss is less than two per cent. 




Fig. 205. 

Since induction is an effect of changing currents only, trans- 
formers have no application to steady currents but find then- 
most useful employment in connection with alternating currents. 
They will therefore be discussed further when that subject is 
reached. (Par. 649.) 

432. Self-induction. — The induction considered in the preced- 
ing pages and revealed by E. M. F. induced in one circuit by vary- 
ing the field of another and neighboring current, is called mutual 
induction. Induction is, however, still more general and inductive 

effects are pro- 
duced in a circuit 
by varying the 
field produced by 
the current flowing 
in the circuit itself. 
This phenomenon 
is called self-induc- 

Fig. 206. tionm 

For example, if a current / be sent around the circular coil A B 
(Fig. 206), a field will be produced within this coil in the direction 




ELECTRO-MAGNETICS. 337 

H. But, we have seen (Par. 421) that if lines of force be thrust 
into this coil in the direction H, there will be induced an E. M. F. 
in the direction E B , that is, opposed or counter to the original 
E. M. F. Therefore, the effect of self-induction is to oppose any 
increase in the current, and this explains why when a circuit is 
closed the current is retarded and does not instantly rise to its 
full value. It is also seen that if a current flowing in this circuit be 
decreased, the self-induction of the circuit delays this decrease 
and causes the current to linger, so that, in general, we may say 
that self-induction tends to prevent any change in the field em- 
braced by a circuit and, consequently, in the current flowing in 
the circuit. 

If a piece of soft iron be inserted in the coil AB, the strength of 
the field H is greatly increased (Par. 390) . Hence, the induction 
of a circuit embracing a magnetic" substance is very much greater 
than the induction of the circuit alone. 

433. Measure of Self-induction. — Since induction is common to 
all circuits and since, especially in dealing with alternating cur- 
rents, it must frequently be taken into account, it is necessary 
that we should have some definite measure of this property and 
some concrete unit by which we may give concise expression to 
its value. 

If we had to deal with circular coils, each of a single turn, we 
could use the term "induction" in its primitive significance of 
"crop of lines of force produced" (Par. 400), and could measure 
induction by the change in the number of lines embraced by the 
coil when the current was increased or decreased one unit. But 
this simple conception is complicated by the fact that the induc- 
tive effect varies with the geometric form of the circuit. For 
example, suppose that in a given circular coil of wire an increase 
of one unit in the current should increase by two the number of 
lines embraced. If the wire be now coiled into two smaller circles, 
but otherwise not changed, an increase of one unit in the current 
would again add two lines, but these two lines would penetrate 
each turn of the coil and the counter E. M. F. produced would 
be twice that produced in the original circuit. Finally, if the wire 
be folded at its middle point and then made into a coil (Par. 315) 
the unit current would again produce the two lines but they would 
be in opposite directions and hence (b, Par. 418) the resultant 
field would be zero and there would be no counter E. M. F. pro- 



338 ELEMENTS OF ELECTRICITY. 

duced. It is agreed, therefore, to use the term "induction" in the 
sense of "cutting of lines of force." Thus, in the illustration above, 
if two lines be cut twice, the cutting is four, and in the last case 
the cutting is zero. From this point of view, therefore, the 
absolute unit of self-induction is the induction of that circuit in 
which a change of one absolute unit of current produces a cutting 
of one line of force. This unit has received no name. The prac- 
tical unit of self-induction, however, is called the henry and is 
defined as the induction of that circuit in which a change of one 
ampere in the current produces a cutting of one hundred million (10 8 ) 
lines of force. The henry is therefore 10 9 absolute units of self- 
induction. 

In the above definition, the question of time is not involved, 
that is, it is immaterial whether the change takes place rapidly or 
slowly. 

434. Inductance. — The total cutting of lines of force caused by 
a change of one ampere in a circuit is called the inductance of the 
circuit and is represented by the symbol L. It follows that if the 
current change / amperes, the total cutting of lines of force will 
be N = LI. If this change takes place in t seconds, the average 
rate of cutting will be N/t or Ll/t, which, as we have seen (Par. 
425) is the counter or back E. M. F. produced in the circuit. This 
may be expressed thus 

E B =-~LI/t 

the negative sign indicat- 
ing that the induced E. M. F. is opposed to the impressed E. M. F. 
In order that E B should be expressed in volts, the above must be 
put in the form 

Es= ~ L -Wxt 

If, however, as is usually the case, L be expressed in henrys 
(cutting of 10 8 lines), this reverts to the form 

E B =-LI/t 

If in this last expression I be one ampere, t be one second and 
Eb be one (negative) volt, L becomes unity, whence we may say 
that a circuit has an inductance of one henry if, when the current is 
varied at the rate of one ampere per second, an opposing E. M. F. of 
one volt is set up in the circuit. 



ELECTRO-MAGNETICS. 339 

If the current does not vary at a uniform rate, the instantaneous 
value of the counter E. M. F. is 

*— *■§ 

This is true for simple coils, since the field of a coil varies 
directly with the current, but it is not strictly true of coils with 
magnetic cores, because with such coils the field does not so vary 
(Par. 393). 

435. Expression for Inductance of a Coil. — An expression for 
the inductance of a coil may be deduced as follows: If a change 
of / amperes in the current flowing in the coil varies the field of 
the coil by <p lines of force, and if the coil consists of N turns, the 
total cutting is 4> N. If this takes place in t seconds, then 

EB =-iwxi Y0lts 

But in the preceding paragraph we saw that 

E B =-LI/t volts 

L being the inductance of 
the circuit in henry s. Equating these expressions and striking 
out common factors 

L1 - 10 8 TO 

In Par. 400 it was shown that the flux produced by a current 
of / amperes in a coil of N turns, I centimeters long and of r 
centimeters radius, wrapped upon an iron core of permeability 
jjl is 

4irNlTrr 2 - 



4:TNIirr 2 n 



10. 1 

This was deduced under the supposition that the core was 
ring-shaped, but it may without great error be applied to coils 
with straight cores. Substituting in (I) above and striking out 
common factors, we have 

T _47r 2 iV 2 r^ 
L ~ Wl 

L being the inductance of the coil in henrys. 

Had the core been of air or other non-magnetic substance,. 
jjl in the above expression becomes unity. 



340 ELEMENTS OF ELECTRICITY. 

436. Helmholtz's Equation.— If an E. M. F. E be impressed 
upon a circuit of resistance R, the current produced will, by 
Ohm's law, be E/R amperes. If, however, there be inductance 
in the circuit, a counter E. M. F. of L . dl/dt volts will be produced 
(Par. 434). This, if acting alone in the circuit, would produce a 
current of 

L dl 
"RW amperes 

The current actually produced is therefore 

T E L dl m 

I = R-RTt amvere " (I) 

If E and L are constant, the variables in this expression are 
/ and t. By transposing and dividing, (I) may be put in the form 

Z* = F^~ (II) 

R~ J 

The integral of the first member is -y-. The integral of the 
second member is — log ( -^ — / ) + a constant, whence 

—j- = — log (d — I ) + a constant (III) 

To find the value of the constant, place t = 0. The first member 
becomes zero, and / disappears from the second member, for at 
the instant t = 0, no current is flowing. The constant there- 
E 



re = log^> 






Substituting in (III) and changing signs throughout, 


R.t , IE T \ , E 


= log 


R 
E 
R 





ELECTRO-MAGNETICS. 



341 



Whence 



^-1 
R 

E 

R 



Rl 



e being 2.7183, the 
base of the natural system of logarithms. Solving for /, 



or 



-it--*) 
-j(i-a 



(IV) 



From this equation, first deduced by Helmholtz, we may 
determine the instantaneous value J of a current in a circuit of 
resistance R and inductance L at any time t after the circuit is 
closed. If the inductance of the circuit be very small, that is, 
if L be very small as compared to R, the second term in the 
parenthesis in (IV) disappears and the current rises almost 
instantly to its maximum value. If, however, the inductance be 

iO 
9 
8 

7 
u 6 

a: s 

£4 

Z 
1 

iO ZO 30 AO SO 60 

SECONDS 
Fig. 207. 

great, as in the case of the coils around a large electro-magnet, 
the rise of the current may be gradual. This is shown graphically 
in Fig. 207 in which the curves represent the growth of the current 
urged by an E. M. F. of ten volts through circuits of a resistance 
of one ohm and inductances of one, ten and twenty henrys, 
respectively. If the inductance be one-tenth of a henry, the 
current at the end of one second will have reached a value of 
9.9996 amperes, while with an inductance of 20 henrys. this 
value is not reached in three minutes. 



/ 








____ 




•rs?" 








X 




-v?* 5 " 






■" 










/ ^ 










/ y 










.'.>-■ 










>'' 










V 










1 











342 ELEMENTS OF ELECTRICITY. 

437. Induced E. M. F. at Make and at Break.— The E. M. F. 

induced when a circuit carrying a current is broken, is, on account 
of the great rapidity with which the lines are removed, much 
greater than that induced when the circuit is closed, or made. 
Interesting experiments have been devised to show this but the 
following considerations will show that they are hardly needed. 

First, when the wires attached to the terminals of an ordinary 
dry cell are touched together, an E. M. F. is induced counter to 
the E. M. F. of the cell. Reflection will show that it must be less 
than the E. M. F. of the cell (that is, less than about 1.4 volts), 
for if it were greater, a reverse current would be sent through the 
cell, and if it were equal, no current would flow, both of which 
suppositions are absurd. 

Second, when the wires are separated, the E. M. F. induced is 
many times greater than that of the cell, for it throws a spark 
across the gap which the E. M. F. of the cell itself could not 
do. 

438. The Induction Coil. — In gasoline engines, the mixture of 
vapor and air, in the proper proportions to produce the most 
powerful explosion, is introduced in the cylinder and must be 
ignited just as the piston is at the proper point in its stroke. The 
ignition of this explosive mixture is generally brought about by 
an electric spark. We have seen (Par. 93) that to produce a 
spark across a gap of even one-hundredth of an inch requires at 
least 300 volts, and this is considerably increased by the pressure 
of the vapor in the cylinder. It would be impracticable to trans- 
port in an automobile a battery large enough to supply this 
voltage direct, but, by utilizing the principle of the transformer 
as applied in an induction coil, the necessary voltage may be 
obtained from two or three cells. 

The induction coil, shown diagrammatically in Fig. 208, con- 
sists of a cylindrical core A (made of a bundle of soft iron wire 
so as to avoid eddy currents), upon which is wrapped the primary 
coil, a few turns of heavy wire, and on top of this, the secondary 
coil, usually many thousand turns of fine wire. In the large 
induction coil of the Military Academy, the primary consists of 
208 feet of one-sixth inch copper wire and the secondary of 49.3 
miles of wire, 1/133 of an inch in diameter. In the circuit of the 
primary there is a battery B of two or three cells, a key K, and 
an interrupter /, similar to the one described in Par. 410. The 



ELECTRO-MAGNETICS. 



343 



ends of the secondary terminate in the adjustable spark gap S. 
If used for ignition purposes, the spark gap is located in a spark 
plug which is screwed into the cylinder of the engine. 

The operation of the coil is as follows: When the key K is 
closed, a current flows through the primary circuit and establishes 
a field from right to left through the coil. The core A becomes 
magnetized and attracts the armature of the interrupter /, thereby 
breaking the circuit. The effect of breaking the circuit is to with- 
draw suddenly the flux through the core and this induces in the 



CM> 



<?-o 




Fig. 208. 

secondary a direct E. M. F. which (Par. 431) is as much greater 
than the E. M. F. of the primary as the number of turns in the 
secondary is greater than the number in the primary. In other 
words, the coil acts as a step up transformer. The voltage in the 
secondary is high enough to cause a rush of sparks across the 
gap S. When the circuit is restored at the interrupter, the current 
again flows through the primary and re-establishes the field in 
the coil, but the induced E. M. F. at make is much less than that 
at break (Par. 437), and sparks are not generally produced. 

To cause the production of sparks when the piston is at the 
proper point in its stroke, the key K is closed by a revolving cam, 
a part of the engine. 

It should be remarked that the invention of the induction coil 
antedates by many years the invention of internal combustion 
engines, and that these coils have other important uses besides 
that of ignition. 

439. Use of Condenser. — The action of an induction coil is 
much improved by shunting across the break of the interrupter 



344 



ELEMENTS OF ELECTRICITY. 



a condenser, shown diagrammatically at G in Fig. 208. A correct 
explanation of its operation involves a discussion of capacity, as 
will be shown when the subject of alternating currents is reached. 
For the time being, however, the following explanation will 
suffice. As preliminary thereto, we assume that (a) the charge 
which may be given to a condenser varies with its capacity and 
with the difference of potential between its terminals (Par. 93), 
and (b) the induced E. M. F. at break is a hundred or more times 
greater than that at make (Par. 437). 



o-O — — O-o 




Fig. 208a. 

Fig. 208a gives in still more diagrammatic form the induction 
coil represented in Fig. 208, the primary and secondary coils 
being shown on separate portions of the core. At make, the 
current flows across AB and through the primary, establishing a 
flux in the core in the direction of the arrow F. There is no 
charge in the condenser G, since A and B are in contact. At 
break, A and B are pulled apart, the self-induced E. M. F. is a 
hundredfold greater than that of the battery and in the same 
direction, there is a corresponding momentary increase in the 
current through the primary and in the flux F. Moreover, since 
A and B are now apart and since the difference of potential be- 
tween them is now great, the condenser G receives a charge. 
The induced E. M. F., however, persists for a very minute interval 
of time, and, as it dies away, the charge can no longer be main- 
tained in the condenser which therefore discharges backward 
through A and the battery to B. This discharge passes through 
the primary with great energy and opposite in direction to the 
original current. It therefore not only pushes out the flux which 
ran from right to left through the core, but establishes a flux in 
this core in the opposite direction, the cutting of lines of force by 
the secondary, and hence the inductive effect, being much greater 
than that produced by simply breaking the circuit in the primary. 



ELECTRO-MAGNETICS. 



345 



At the next succeeding make, the current through the primary 
must rise slowly for, before it can establish a field in the core, it 
must push out the negative field already there. Therefore, the 
condenser suppresses any sparks at make and increases the in- 
tensity of the sparks at break. 




M 




Fig. 209. 

440. The Bell Telephone. — A very important application of 
the principle of induction is the telephone. The original form, as 
invented by Graham Bell in 1876, is shown in section in Fig. 209. 
It consists of a cylindrical, hard-rubber case expanded at one 
end and containing a long bar-magnet M. Just in front of the 
pole of the magnet, but not in contact with it, is a diaphragm D 
of thin sheet iron, similar to that used for tintypes. Around the 
same pole of the magnet is wrapped a coil C whose free ends are 
attached to the terminals T. Wires extend from these terminals 
to the other end of the line and are there attached to a second 
instrument, a duplicate of the first. 

When sound waves strike upon the diaphragm, they set it in 
vibration and it alternately approaches and recedes from the 
magnet. As it approaches the magnet, the air gap between the 
two is reduced and, the diaphragm being of iron, additional lines 
of force extend from the magnet to it. As it recedes, the number 
of lines decreases. Since these lines pass through the coil C, 
variations in their number set up induced currents in the coil, 
and hence in the circuit of which it forms a part. As these currents 
flow in one direction through the coil at the far end of the line, 
they increase the strength of the enclosed magnet and the dia- 
phragm is drawn in. As they flow in the opposite direction, they 
weaken the magnet and the diaphragm springs back. The 
vibrations at the near end of the line are therefore reproduced at 
the far end, and this causes the sounds to be repeated. It is thus 



346 



ELEMENTS OF ELECTRICITY. 



seen that the Bell telephone was originally intended to be used 
both as a transmitter and as a receiver. As a transmitter, it was 
used as a mouth -piece; as a receiver, it was held to the ear. In 
more recent receivers, instead of a simple bar-magnet as described 
above, a slender horseshoe magnet with soft iron pole pieces is 
used, but the principle is the same. 

441. The Transmitter.— The E. M. F. induced by the vibra- 
tion of the diaphragm of the Bell telephone is necessarily very 
small. The current which it can drive over a long line of con- 
siderable resistance is therefore very feeble, so feeble in fact as 
to restrict its use to short distances. This difficulty was first 
overcome by the Blake transmitter. More recent transmitters 
embody the same principle but are improved in details. A 




Fig. 210. 

typical form is shown diagrammatically in section in Fig. 210. 
It consists externally of a metal case with a suitably shaped hard- 
rubber mouth piece. Within, there is a diaphragm, insulated 
from the case, and a cylindrical metal box. In the back of this 
box there is a carbon disc and in the front a second, the space 
between the two being packed with carbon granules. The front 
carbon disc is bolted to the diaphragm. The sides of the box are 
lined with insulating material. A wire connected to the diaphragm 
runs to a battery of several cells, whence the circuit is completed 
through the primary of a small step up transformer, thence 
through the metal frame supporting the transmitter back to the 
enclosed metal box, through the back carbon disc, through the 
carbon granules to the front carbon disc and thence to the dia- 
phragm. There is an arrangement, shown in Fig. 211, by which 
this circuit is broken when the telephone is not in use. When the 



ELECTRO-MAGNETICS. 



347 



telephone is in operation, a current flows through the circuit but 
the resistance of the carbon granules is large and the actual 
amount of the current is small. When the diaphragm is set in 
vibration by the sound waves, it compresses the granulated car- 
bon which, as we have seen (Par. 285), reduces the resistance of 
the carbon and allows a greater current to flow from the battery 
through the primary. The current through the circuit therefore 
varies with the sound waves and the voltage in the primary is 
stepped up by the transformer so that the resistance of the line, 
the secondary, may be overcome. The transmitter is seen to be 
somewhat analogous to the relay used in telegraphy (Par. 412). 



W///////////777> 



vzzza 



boo 



BELL 




Fig. 211. 
442. Operation of Telephone. — From the foregoing, each tele- 
phone consists of a receiver, a transmitter, a transformer and a 
battery. It must include some device, usually a bell, by which 
calls may be received, and also some arrangement by which other 
stations may be called. Finally, when the telephone is not in use 
the circuit of the battery must be broken, otherwise the battery 
would soon run down. 



348 ELEMENTS OF ELECTRICITY. 

There are many telephone systems in use. Fig. 211 represents 
a common form, the hinged doors of the boxes being shown as 
swung to one side. Its operation is as follows: 

(a) To call a station. With the receiver on the hook switch, 
as represented, the crank handle A of the magneto is turned. 
(The magneto is a small generator whose operation will be ex- 
plained in Part V.) A current traverses the following path: 
B-C-D-E-F-G-H-J-K-L. At the second station D, the circuit 
is precisely the same and the bell rings at both stations. " 

(b) To receive a message. The receiver is removed from the 
hook and held to the ear. The hook, freed from the weight of the 
receiver, rises and breaks the circuit at G but closes it at M, N 
and 0. The current coming in from D follows the route 
E-F-O-R-S-B-C. 

(c) To send a message. The hook being up, the transmitter- 
battery-primary circuit is closed at NM. Currents through this 
circuit are stepped up in the secondary S and follow the route 
given above. 



ELECTRO-MAGNETICS. 349 



CHAPTER 34. 

AMMETERS AND VOLTMETERS. 

443. Electrical Quantities to be Measured. — The modern 
development of the science of electricity has been accompanied 
and greatly aided by the production of ever improving instru- 
ments of precision for the rapid and accurate measurement of 
certain electrical quantities. The principal of these quantities 
are: 

1 Resistance, 

2 Strength or intensity of current, 

3 Electro-motive force, 

4 Electrical power. 

The measurement of resistance was explained in Chapter 26 
and in the present chapter we are concerned with the measure- 
ment of current and of electro-motive force. 

444. Electrical Effects Used in Measurements. — Electricity 
not being matter, and hence being imponderable and without 
physical dimensions, must be measured indirectly by its effects. 
These are usually classed under four heads, viz.: 

1. Thermal. — A current flowing through a conductor heats it. 

2. Electro-magnetic. — A current flowing through a conductor 
produces about it a magnetic field, (a) If flowing near a poised 
magnetic needle, the needle will be deflected, or, (b) if flowing 
around a soft iron core the latter will be magnetized. 

3. Electro-chemical. — (a) A current flowing through acidulated 
water will decompose the same, releasing its component gases 
hydrogen and oxygen, or (b) flowing through a solution of a 
metallic salt will decompose the salt, depositing the metal upon 
the cathode or plate by which the current leaves. 

4. Physiological. — A current flowing through a living or recently 
living body will produce certain effects such as muscular twitchings 
and contractions, and in a living being cause more or less painful 
sensations. 



350 



ELEMENTS OF ELECTRICITY. 



Of the above, the first three may be and are used in electrical 
measurements. 

445. Effect Best Adapted for Measurement. — The effect best 
adapted for measurement may be arrived at by a consideration 
of the following experiments after Professor Ayrton. In Fig. 212 




Fig. 212. 

B represents a battery with which are connected in series the 
various pieces of apparatus 1, 2, 3, 4, and 5, through which there- 
fore the same current flows. 

1 is a thermometer around whose bulb the conducting wire is 
wrapped and which dips into some oil, a non-conductor of 
electricity. 

2 is a magnetic needle in whose vertical plane and around 
whose pivot as a center the wire is bent in a circle. 

3 is a soft iron core around which the wire is wrapped. On top 
of this core is a piece of soft iron fastened to the hook of a spring 
balance. 

4 is a glass jar upon which is screwed an air-tight cover. Through 
this run the two wires, each terminating in a platinum plate 



ELECTRO-MAGNETICS. 351 

dipping into the acidulated water with which the jar is partly 
filled, and also a glass tube extending nearly to the bottom of the 
jar, its upper portion expanded and graduated as shown. 

5 is a glass jar partly filled with a solution of copper sul- 
phate into which dip two copper plates to which the wires are 
attached. 

If now the key be closed and the current be allowed to flow for 
a short time, t, the following effects will be noted : 

1. The thermometer will indicate a rise in temperature. 

2. The needle will be deflected through a certain angle and will 
remain constantly at that angle as long as the current flows. 

3. The soft iron core will become magnetized and will attract 
the iron block so that a force of x ounces must be exerted upon 
the spring balance to tear the block free. 

4. Gas will be released at the surface of the two platinum plates 
in 4 and its pressure will force a certain number of cubic centi- 
meters of the liquid up into the graduated tube. 

5. The cathode copper plate in 5 will be found to have increased 
in weight due to the deposition of fresh copper upon its surface. 

446. Second Experiment. — If, beginning under the original 
conditions of the preceding experiment, the key be closed an 
interval, t', say twice as long as the original t, the following will 
be observed: 

1. The thermometer will indicate a temperature in general 
greater than that produced by the first experiment but bearing 
no definite relation to the same. 

2. The needle will be deflected through the same angle as before. 

3. The same pull will be required to release the soft iron block 
from the electro-magnet. 

4. Twice the volume of gas will be released in 4. 

5. Twice the weight of copper will be deposited on the cathode 
in 5. 

Assuming that the current has been the same in these two 
experiments, we may conclude — 

(a) That the temperature indicated by the thermometer in 1 
varies in some indeterminate manner with the time and that 
consequently the heating effect is not suitable for measurement. 



352 



ELEMENTS OF ELECTRICITY 



(b) That the electro-chemical effects vary directly with the 
time and hence if reduced to a common unit of time will give a 
definite measure. 

(c) That the electro-magnetic effects are independent of time 
and give a direct measure without reduction. 

447. Third Experiment.— A third experiment will throw further 
light upon this subject. 

In Fig. 213 B represents, as before, a battery. 




Fig. 213. 

1 and 1A thermometers, as before, but 1A has more turns of 
the wire around its bulb than has 1 and they may be in different 
sized jars which contain different amounts of oil and perhaps 
different kinds of oil. 

2 and 2 A magnetic needles with circular coils in their vertical 
plane, the coil around 2 being of less diameter and of a greater 
number of turns than that around 2 A. 

3 and 3 A electro-magnets differing in size and in the number 
of turns of the wire. 

4, 4A and 4B gas voltameters, 4 being two in parallel, 4A a 
large one with plates far apart, 45 a small one with plates closer 
together. 



ELECTRO-MAGNETICS. 



353 



5, 5A and 5B copper voltameters arranged similarly to the gas 
voltameters. 

The key now being closed for an interval t, during which the 
same current flows through the entire system, the following will 
be observed: 

1. The two thermometers will indicate a rise of temperature 
but the indications will not be the same and will bear no apparent 
relation to each other. 

2. The magnetic needles will be deflected and will remain 
constantly deflected as long as the current flows but the angles 




Fig. 213. 

will differ in the two cases and will bear no apparent relation to 
each other, except that the deflection is greater in the instrument 
with the greater number of turns. 

3. The electro-magnets will require pulls of x and y ounces 
respectively to separate the iron blocks but these pulls will bear no 
apparent relation to each other. 

4. The amount of gas released in each of the two gas voltameters 
in series and the sum of the amounts released in the two in parallel 
will be exactly equal. 

5. The amount of copper deposited in each of the two copper 
voltameters in series and the sum of the amounts deposited in 
the two in parallel will be exactly equal. 



354 ELEMENTS OF ELECTRICITY. 

We conclude from the above: 

(a) That the heating effect is unsuitable for measurement. 

(b) That the electro-magnetic effect, while constant for the 
same current for any one instrument, is yet a function of the 
mechanical arrangement of the instrument and would be different 
for every different instrument. 

(c) That the electro-chemical effect is, within wide limits, inde- 
pendent of the size, shape, and arrangement of the instruments. 

448. Electro -Chemical Effect Selected as Standard. — As a 

logical consequence of the above, the electro-chemical effect has 
been selected as a standard for the measurement of electrical 
currents and the Act of Congress of July 12, 1894, legalized the 
resolution of the International Congress of Electricians of the 
preceding year and defined the practical unit of current, the 
ampere, as that unvarying current which flowing through an 
aqueous solution of nitrate of silver deposits silver at the rate 
of .001118 gram per second. 

449. Why Silver Selected. — The current is defined in terms of 
silver deposited, partly because silver is one of the precious metals 
and when deposited from solution can be dried and weighed with- 
out appreciable error due to increase of weight by oxidation or 
other chemical change, but mainly because it combines high 
atomic weight (107.9) with mono valency while the next most 
suitable metal, copper, whose atomic weight is 63.6, is bivalent, 
so that a given current flowing for a given time will deposit nearly 
three and a half times as great a weight of silver as of copper. 
Silver is therefore used in delicate measurements of small currents 
but it is expensive and for large currents copper is employed. 

450. Reason for Weight Selected. — It may naturally be asked 
why this particular weight of silver was selected instead of some 
even number, such as .001 gram for instance. The reply to this 
is that the absolute C. G. S. unit of current had already been 
defined, the definition being based upon electro-magnetic effects 
(Par. 355), and from many elaborate and accurate experiments 
the amount of silver deposited by the unit current, and hence the 
amount deposited by an ampere, had been determined. 

451. Unsuitableness of Electro- Chemical Effect for Industrial 
Needs. — While, as shown above, the electro-chemical effect is 
selected as a standard, in its practical application to most in- 



ELECTRO-MAGNETICS. 355 

dustrial needs it has certain insuperable objections. The principal 
of these are (a) time consumed in a determination and hence 
inability to take instantaneous observations and (b) lack of sensi- 
tiveness and hence inability to measure small effects. 

(a) For example, just as the steam engineer must without inter- 
mediate calculations be able to read his steam gauge at any 
moment, so the electrician should be able to read at any instant 
his voltage and current. The determination of a current by a 
voltameter observation is a laborious matter of hours, while what 
is needed is an instrument which can be read just like a steam 
gauge instantly and with a minimum expenditure of labor. To 
make another comparison, to use a voltameter is as if a person 
desiring to find out the time was compelled to take a set of astro- 
nomical observations and by tedious calculations arrive at his 
result. Naturally it is simpler, and in most cases preferable, to 
read from a clock even though it should be several minutes fast 

'or slow. 

(b) Again, the sensitiveness of a voltameter is not great and 
can hardly be increased. Many currents with which electricians 
have to deal are so small that they would have to flow for days 
before they would produce enough chemical effect to be suscep- 
tible of accurate measurement and even this supposes what is 
very doubtful, that is, that a current could be kept constant for 
that length of time. 

452. Electro- Magnetic Effect Best for Practical Measurements. 

— As we saw in the account of the preliminary experiments in 
Pars. 445, 446, and 447, the magnetic needle in each case 
instantly took up a certain position and retained it as long as the 
current remained constant. This then is the basis of the majority 
of instruments in practical use. 

453. Why not Selected as Standard. — The question now arises 
why then was not the electro-magnetic effect selected at the 
outset as the standard. The reply is that it is well-nigh impossible 
to construct two galvanometers which shall be duplicates, and it 
would be even more difficult to construct a duplicate following 
the specifications which such a definition would have involved. 
On the other hand, as we have seen above, the electro-chemical 
effect is, within wide limits, independent of instrumental size and 
shape and accurate measurements can be made with such appara- 



356 ELEMENTS OF ELECTRICITY. 

tus as is found in any laboratory. An instrument maker could 
therefore accurately calibrate a galvanometer by the somewhat 
tedious voltameter method, as explained in the next paragraph, 
and thereafter use this calibrated galvanometer as a standard for 
the rapid calibration of others. 

454. Calibration of Galvanometer. — The galvanometer to 
measure current is calibrated by connecting it in series with a 
voltameter, noting the point at which the needle stands, deter- 
mining the current by means of the voltameter and marking the 
galvanometer scale to correspond, then repeating this, varying 
the current, and so on. 

For small currents it is not possible to calibrate the galvanom- 
eter directly by this method, but since galvanometers follow the 
fixed law that the deflecting force is directly proportional to the 
number of turns in the coil, it may be calibrated as follows. It 
is first calibrated for large currents as explained above, with say 
only one turn in the coil. The coil is then re-wrapped with finer 
wire and say 100 turns are put on. A small current is now sent 
through the coil and produces a deflection which corresponds to i 
amperes in the original calibration. We know that the effect of 
the actual current has been multiplied 100 times by the number 
of turns, consequently the current is actually only i/100 amperes 
and the scale can be so marked, and so on. 

The sensitiveness of a galvanometer can be increased to a very 
high degree. Ayrton states that it is possible to measure accurate- 
ly with one a current so small that it would have to flow for a 
million years through a voltameter before it produced as much 
chemical action as a current of one ampere could produce in one 
hour. 

455. Difference between Ammeters and Voltmeters. — The 

galvanometers used to measure current are called Ammeters; 
those to measure voltage are called Voltmeters. The moving parts 
of an ammeter and of a voltmeter, of the kind shortly to be 
described, are indistinguishable. They both move under the effect 
of the current which flows through them. Ohm's law can be 
written E = RI. As applied to a voltmeter or to an ammeter, R 
is the instrumental resistance and is constant, whence it is seen 
that the voltage is always some constant times the current through 
the instrument and it might be thought that one and the same 



ELECTRO-MAGNETICS. 357 

instrument could be used either as a voltmeter or as an ammeter. 
If its scale were graduated in amperes, the readings need only be 
multiplied by the constant R to convert them to volts, or there 
might perhaps be two parallel scales under the same needle, one 
reading amperes and the other volts. If, as will be shown later 
(see Par. 474), an additional piece of apparatus be employed, the 
foregoing conclusion is correct, but alone, ammeters and volt- 
meters are not interchangeable. The following explanation of 
their use will make it clear why they are not. 

456. Essential of Measuring Instruments. — The first require- 
ment of every measuring instrument is that when used it should 
not alter the quantity which it is to measure. Consequently, 
neither the ammeter nor the voltmeter when properly connected 
should change the resistance in the original circuit. Should this 
resistance be changed, the current will change in accordance with 
Ohm's law and this will also involve change in voltage. It is 
interesting to see how these two instruments fulfill this require- 
ment by apparently diametrically opposite methods. 

457. Ammeters. — An ammeter measures the current flowing 
in the circuit at the point at which it is connected. It is inserted 
in series in this circuit and should it have any appreciable resist- 
ance it would reduce the current, that is, change the quantity 
it is to measure. The resistance of an ammeter must therefore 
be so small that its effect on the current is negligible. 



B 



<!.ji|i| 



j VOLTMETER 



<—Q 




Fig. 214. 

458. Voltmeters.— A voltmeter measures the difference of po- 
tential between the two points to which it is connected. These 
two points are never adjacent but in general are far apart elec- 
trically. For example, they may be the terminals of a battery 
(Fig. 214) or the brushes of a dynamo or the leads of an electric 
light circuit. Two cases may arise: (a) there may be a broken 
circuit between the two points, or (b) there may be between them 



358 ELEMENTS OF ELECTRICITY. 

a closed circuit over which a current is flowing. In either case, in 
order that the original status of the circuit as regards current 
should be changed as little as possible, the resistance of the volt- 
meter must be great. 

(a) If the circuit between the two points be broken, the resist- 
ance between them may be considered as infinite, and no current 
flows. When the voltmeter is inserted, therefore, its resistance 
must be so great that the current which flows through it is so 
small as to be negligible. 

(b) If a current is flowing between the two points, in order that 
it may be inserted between them and yet not disturb the original 
circuit, the voltmeter must be connected in shunt. The voltmeter 
and the original circuit are therefore in parallel and constitute a 
divided circuit whose resistance is less than that of the original 
circuit (Par. 293). In order to alter the original resistance as 
little as possible the resistance of the voltmeter must be as great 
as possible. This statement hardly requires proof but may be 
shown mathematically as follows: let R be the resistance of the 
original circuit between the two points and x be the resistance of 
the voltmeter. The joint resistance is (Par. 293) 

Rx 



This may be written 



R- 



R -\-x 
R* 



R +x 



whence it is seen that the joint resistance is less than the original 

r>2 

resistance by the fraction „ and approaches the original 

Mir ~l X 

resistance as this fraction approaches zero, which it does as x 
increases. 

Practically, the resistance should not be made excessive for 
enough current must be let through the voltmeter to actuate the 
moving parts. The average resistance of a voltmeter reading up 
to 100 volts is about 15,000 ohms. 

459. Summary. — To sum up — 

(a) The moving parts of an ammeter and of a voltmeter are 
the same. 



ELECTRO-MAGNETICS. 359 

(b) An ammeter is always connected in series and its resistance 
should be as near zero as possible. 

(c) A voltmeter between two points in a circuit carrying a 
current must always be connected in shunt and its resistance 
should be great, so great that the current through it is neg- 
ligible. 

460. Numerical Example, Voltmeter Between Two Points of 
a Circuit. — The following numerical example will bring out the 
effect of altering the resistance of a voltmeter. 

Suppose we wish to measure with a voltmeter the difference of 
potential between AB, the terminals of the battery represented 
in Fig. 214. Suppose the E. M. F. of the battery to be 10 volts, 
the internal resistance to be 1 ohm, the external resistance 9 ohms. 

rr 1 A 

The current is -r^— — = ~ , ., = 1 ampere. The internal drop is 
R + r 9 + 1 

It = 1 X 1 = 1 volt, hence the difference of potential between 

A and B is 9 volts. To measure this we connect up as shown. 

Suppose the resistance of the voltmeter to be 9 ohms. The joint 

resistance between A and B is now 9/2 =4.5 ohms, the current 

is . - .. =1.8+ amperes and the difference of potential between 

A and B is 4.5x1.8=8.1 volts or 0.9 less than it was before the 
voltmeter was connected up. 

Suppose the resistance of the voltmeter to be 91 ohms. The 

external resistance becomes Q Q1 = 8.19 ohms and the current 

1.08 + amperes. The difference of potential between A and B 
is now 1.08 X 8.19 = 8.85 volts, or only .15 volt less than the 
original voltage. 

Again, increase the resistance of the voltmeter to 991 ohms. 
The external resistance becomes 8.919, the current, 1.008 and 
the difference of potential between A and B, 1.008 X 8.919 = 8.99 
volts, or only .01 less than the original voltage. 

The scales of voltmeters, even of small range, are hardly ever 
graduated closer than to the nearest tenth and by estimate the 
position of the needle can be read to the nearest hundredth, there- 
fore the above reading is within the limits of accuracy of the 
instrument. A further increase in the resistance would still 
further increase the theoretical accuracy. The resistance of the 



360 



ELEMENTS OF ELECTRICITY. 



usual voltmeter is considerably greater than the 991 ohms assumed 
above. 

461. E. M. F. of a Cell or Battery.— Let Fig. 215 represent a 
cell or battery whose E. M. F. is E and whose internal resistance 
- + 




Fig. 215. 

is r, and suppose it to be connected up with a voltmeter whose 
resistance is R. The current through the circuit is by Ohm's law 

R + r 

which obviously decreases 
as R increases. The above may be written 

IR + Ir = E 

whence IR = E — Ir 

But IR, the external drop, is what the voltmeter reads and this 
is always less by the quantity Ir, the internal drop, than E, the 
total E. M. F. However, this internal drop decreases as I gets 
smaller, and we have shown above that / gets smaller as R, the 
resistance of the voltmeter increases, therefore, the greater the 
resistance of the voltmeter, the more nearly the latter will read 
the E. M. F. of the cell or battery. 

462. Classification of Ammeters and Voltmeters. — Ammeters 
and voltmeters may be classified in a number of ways. 

1st, according to the kind of current for which they are intended 
as those for 

(a) Direct Current, 

(b) Alternating Current. 

Some alternating current instruments may, by taking certain 
precautions, be used with direct currents but direct current 
instruments can not be used with alternating currents. 



ELECTRO-MAGNETICS. 361 

2d. according to the principle upon which they work, as 

(a) Hot Wire Instruments, 

(b) Moving Iron Instruments, 

(c) Moving Coil Instruments, 

(d) Induction Instruments. 

3d, according to the controlling force, as those with 

(a) Gravity Control, 

(b) Spring Control, 

(c) Magnetic Control. 

Bifilar control, control by torsion and control by the earth's 
magnetism can not be used in these instruments and gravity 
control is unsuitable for the portable class. 
4th, according to the manner of their use, as 

(a) Portable, 

(b) Switchboard. 

5th, according to the arrangement of their scales, as 

(a) Dial Instruments, those whose pointer moves over an arc 

of a circle like the face of a clock. 

(b) Edgewise Instruments, the scale being on the surface of a 

cylinder which may be either horizontal or vertical, the 

pointer moving parallel to the elements of the cylinder. 

They occupy less space on the switchboard than the dial 

instruments. See Fig. 227. 
Dial scales and horizontal edgewise scales usually have the zero 
on the left, but for some purposes it is of advantage to have the 
zero at the center although this shortens the available scale length 
by one-half. For instance, a zero center ammeter may be used to 
measure the current used in charging a storage battery and also 
the current given out in the opposite direction by the battery 
on discharge. 

The number of kinds is so great that the mere enumeration of 
them would be voluminous, therefore description will be limited 
to certain typical forms in general use in this country. 

463. Hot Wire Instruments. — In these the current flows 
through a long and thin platinum wire one end of which is fastened 
rigidly, the other directly or through a system of multiplying levers 
to a movable needle. The wire is drawn taut by a spring fastened 
to the needle. When a current flows through the wire it is heated 



362 ELEMENTS OF ELECTRICITY. 

and expands. The slack is taken up by the spring and this causes 
the needle to move over the scale. Since the heating effect varies 
as the square of the current, the divisions on the scales of these 
instruments can not be evenly spaced. They may be used with 
both direct and alternating currents. 

464. Moving Iron Instruments. — These are also called "soft 
iron" and "gravity control" instruments, and are largely used 
abroad and to a less extent in this country. They may be used for 
both direct and alternating currents. There are many kinds, but 
the following will illustrate their principle. Fig. 216 represents 
an end view. C is a hollow cylindrical coil around which the cur- 
rent flows. A is the end of a bar of soft iron attached rigidly to 
the coil or to its frame, its length parallel to the axis of the cylinder. 
B is a second bar of soft iron parallel to the first and attached to 
the axis D, which is free to rotate. P is the pointer and W is an 
adjustable weight of non-magnetic metal, both attached to the 

axis D. The instrument can be used 
in but one position and when the weight 
W is properly adjusted the pointer P 
is on the zero of the scale. Suppose a 
current to flow around the coil; the 
bars A and B inside of the solenoid will 
both be magnetized with their north 
poles in the same direction. They will 
therefore repel each other, B will move 
off to the right, the pointer will sweep 
across the scale and the weight W will 
be lifted and oppose an increasing torque to the movement. 

In a second class of these instruments the moving iron piece is 
drawn into a solenoid around which the current flows. 

Like the preceding, the scales of these instruments can not be 
evenly spaced; moreover, they are liable to error due to residual 
magnetism in the soft iron bars and may give different readings 
for the same current depending upon whether the current has 
previously been increasing or decreasing. These disadvantages 
may more than compensate for the advantage of unvarying 
control. 

465. Need of Ammeter Shunts. — We saw in Par. 457 that an 
ammeter is inserted in series in the circuit and should oppose no 




ELECTRO-MAGNETICS. 



363 



resistance to the current. Some ammeters must measure very 
large currents, so large that the conductor must have a cross- 
section of a number of square inches. It is impracticable to con- 
struct an instrument whose coils should even approach such size, 
therefore the current is divided at the instrument and some very 
small but constant fraction is sent through the coil. This division 
is made by means of a shunt (Par. 301). For small portable 
instruments the shunt is within the case and such are said to be 
self-contained. For larger switchboard instruments the shunt is 
generally a separate piece of apparatus. 

466. Switchboard Shunts. — These are also called "station 
shunts." They consist of two heavy copper terminals A and B, 
Fig. 217, which are connected by one or more strips or sheets C of 




Fig. 217. 

a special alloy of very small temperature coefficient. The strips are 
used, instead of one piece of the same cross-section, so as to offer 
more surface for cooling. On each terminal there is a binding 
screw D and E to which the leads to the instrument, flexible 
insulated wire cords six or eight feet long, are attached. Fig. 218 
shows an ammeter and its shunt in position. 




Fig. 218. 

Suppose the resistance of a station shunt for an ammeter reading 
as high as 5000 amperes to be .00001 ohm; therefore, with full 
current the drop from D to E is .05 volt, and as the resistance of 
the instrument and its leads is .5 ohm, the maximum current 



364 



ELEMENTS OF ELECTRICITY. 



through it is 0.1 ampere. The resistance of the leads is taken into 
consideration in calibrating the instrument and they should on 
no account be altered by lengthening or shortening. They and 
the shunt are numbered to correspond to the instrument with 
which they are to be used and can not be used with any other. 
These leads confer a two-fold advantage; 1st, they permit of the 
position of the ammeter being shifted about at pleasure and with- 
out the expense caused by additional lengths of heavy copper 
mains or the trouble caused by the mechanical labor in bending 
and arranging these mains; 2d, the ammeter can be placed at such 
a distance from the mains that it is unaffected by the field pro- 
duced around them by even very powerful currents. 

467. The Weston D. C. Ammeter. — The Weston instruments 
are both in construction and accuracy among the best. In 




principle they are d'Arsonval galvanometers (Par. 378) with 
certain changes by which, while overcoming the structural weak- 
ness of the d'Arsonval instrument and making it fit for portable 
use, the requisite sensitiveness is retained. These changes are 
(a) substituting for the phosphor-bronze suspension filament 
suspension of the coil by pivots in watch jewels; (b) control by 
coiled hair springs instead of by torsion of the suspending fila- 
ment; (c) use of a pointer of aluminum instead of reflection from 
a mirror; (d) accurate balancing of the coil, enabling the instru- 



ELECTRO-MAGNETICS. 365 

ment to be used in any position; (e) improved damping, making 
the instrument absolutely dead beat (Par. 379). 

They are of many types. One of the usual forms of portable 
ammeter is represented in Fig. 219. Its case is of pressed brass 
or copper mounted upon a wooden base. In the larger switch- 
board instruments the case is of cast iron which has the advantage 
of shielding the instrumental field from perturbations due to 
external fields. 

Within the case and nearly filling it is a permanent horseshoe 
magnet M (Fig. 220). To this are attached the soft iron pole 
pieces N and S which include between them a cylindrical opening. 
Were these pole pieces as represented in a in the following figure 
the greater part of the lines of force would cross the field at the 





Fig. 220. 



points where the horns of N and S approach each other most 
closely. The field would therefore be crowded at these points and 
thin at the intermediate points. However, as shown in b, a soft 
iron cylinder C bolted to a brass cross bar B, which is in turn 
bolted to the pole pieces, is fastened concentrically in the space 
between the pole pieces. The air gap between the cylinder and 
the pole pieces being very small and the permeability of the 
cylinder being large, the lines of force are evenly distributed and 
the field is very uniform (Par. 143). Pivoted in watch jewels so 
as to turn in this air gap is the rectangular coil. It is of very fine 
wire wrapped upon a light aluminum frame. Upon the axis of 
the coil are mounted from top to bottom the upper spiral spring, 
the aluminum needle, and below the coil the lower spiral spring 
coiled in opposite direction to the first. The needle, to combine 
lightness and stiffness, may be in cross-section either tubular or 
like an inverted V. The end which travels over the scale is, in 
portable instruments, compressed sidewise like a knife-blade and 



366 ELEMENTS OF ELECTRICITY. 

in switchboard instruments terminates in an arrow-head. The 
rear end of the needle extends beyond the axis and carries an 
adjustable counterweight. There are also similar weights at 
right angles to the needle and by these the moving parts- are so 
balanced that the instrument may be used in any position. 

The binding posts by which the current enters and leaves may 
be placed, as shown in Fig. 219, both on one side, or may be both 
at the top or may be on opposite sides. For those instruments 
whose zero is at one end of the scale the post by which the current 
must enter is marked conspicuously + as shown in Figs. 219 and 
222. 

In portable instruments with self-contained shunt, the latter 
is a strip of alloy arranged similarly to the switchboard shunt 
described in Par. 466 above. The fraction of the current which 
flows through the coil flows first to the upper coiled spring, around 
this spring to its insulated hub, thence to the coil, around the coil 
and out by the lower coiled spring. Fig. 221 illustrates the actu- 

^ -.^^ ating forces. The lines of force of the 

field run from N to S, the current flows 
up the right hand side of the coil and 
down the left, the lines of force of the 
coil run as shown by the short arrows. 
According to Maxwell's law the coil 
will therefore turn in a clockwise direc- 
tion. Reflection will show that this 
could not be used with an alternating 
current. 

"Pip* 221 

s ' * The field being very uniform and the 

resistance to torsion which the coiled spring offers increasing 
directly with the angle through which the coil turns, the scale is 
regularly spaced. Parallel to the scale and just beneath it is 
fastened an arc of a mirror. By covering the reflection of the 
needle in the mirror by the needle itself, the observer makes sure 
that the eye is always at the same angle with reference to the 
needle and to the plane of the scale and errors due to parallax are 
avoided. 

The aluminum coil frame rotating in the strong magnetic field 
in the narrow air gap makes the instrument very dead beat. The 
damping effect varies as the square of the magnetic strength. 




ELECTRO-MAGNETICS. 



367 



468. Weston Portable D. C. Voltmeter.— This instrument 
closely resembles the preceding. The one represented in Fig. 222 




Fig. 222. 

differs externally in having above the + binding post on the right 
a push-button switch by which the current through the instrument 
may be closed or broken at will, and on the left two binding posts 
by either of which the current may leave. The object of these is 
explained below. Internally it differs in having no shunt but a 
single circuit in which is a resistance coil. Suppose connection 
to be made with upper left hand binding post and circuit com- 




PUSH BUTTON 
<. 



Fig. 223. 

pleted. The current enters on the right (Fig. 223), through the 
button switch, thence through the rotating coil, thence through 
the resistance coil A and out. The resistance of the coil A, in 
the particular instrument represented in the figure, is so adjusted 
that a difference of potential between the terminals of the instru- 
ment of 3 volts will drive enough current through to carry the 



368 



ELEMENTS OF ELECTRICITY. 



needle entirely across the scale. The maximum reading is there- 
fore 3 volts, the scale is graduated and numbered on the lower 
side accordingly, and the corresponding binding post is plainly 
marked 3. 

If connection be made at the lower left hand binding post the 
current after leaving the moving coil passes through the resistance 
coil B and out. The resistance of B is so adjusted that the instru- 
mental resistance is now 50 times greater than before, therefore 
a voltage 50 times greater, or 150 volts, would be required to 
carry the needle entirely across the scale. This binding post is 
therefore marked 150 and the upper side of the scale is numbered 
to correspond. 

The two scales are usually selected so that the larger is ten or 
some multiple of ten times the smaller, therefore the graduation 
of the two scales is the same and it is only necessary to use two 
sets of numbers. 

The resistance through the smaller coil of a 15-150 voltmeter 
of this class was found to be 1772 ohms, that through the larger 
coil 17,720 ohms. 

These instruments are calibrated by comparison, usually 
through a potentiometer, with standard cells. The importance 
of accuracy in calibration will be realized when the statement is 
made that in electric lighting an increase of 3 per cent above 
the normal voltage shortens the useful life of a lamp one-half 
while a decrease of 4 per cent below normal reduces the candle 
power of the lamp one-fifth. 




Fig. 224. 



469. Multipliers. — The foregoing will enable us to understand 
an auxiliary piece of apparatus used with voltmeters and called 
a multiplier. If there be connected in series with a voltmeter, 
as shown in Fig. 224, a resistance MP which is so adjusted that 
the resistance between C and M is ten times what it is between 



ELECTRO-MA GNETICS. 



369 



C and D, to produce a given deflection of the needle will require 
a difference of potential between C and M ten times greater than 
that between C and D. Hence to get the correct difference of 
potential between C and M the readings of the scale must be 
multiplied by ten. Therefore, a multiplier is a resistance which, 
when connected in series with a voltmeter, has the effect of multi- 
plying the value of the scale divisions by a certain factor. This 
factor is usually marked upon the case of the multiplier. 

Multipliers are not interchangeable but must be used with the 
particular voltmeter for which they are constructed. The second 
coil B in Fig. 223 is in effect a self-contained multiplier. 

470. The Weston D. C. A. C. Voltmeter.— Consider Fig. 221 
and suppose the current to be alternating. The direction of the 




Fig. 225. 

field due to the permanent magnet remains constant while that 
through the coil changes with change of direction of the current. 
Hence at one instant the needle would tend to turn in a clockwise 
direction and at the next instant in a counter-clockwise direction 
and if it moved at all would only quiver. Therefore, such instru- 
ments cannot be used with alternating currents. 

The Weston D. C. A. C. voltmeter, to overcome this objection, 
employs the principle of the dynamometer (Par. 382). There is 
no permanent magnet but within the case and perpendicular to 
the middle of the scale arc there is a thin tubular brass frame 



370 



ELEMENTS OF ELECTRICITY. 



around which are wrapped many turns of fine wire. This cylinder 
is separated into two parts by a narrow gap in its middle (shown 
diagrammatically and much exaggerated in Fig. 225) and in this 
gap there turns a vertical axis which carries the needle, controlling 
spiral springs, movable coil, etc., as in the instruments already 
described. The movable coil C is circular instead of rectangular 
and normally its plane makes an angle of 45° with the axis of the 
cylinder. The current enters at E, flows around the coil A, thence 
to the upper spiral spring, then around the movable coil but 
opposite to its direction around A, thence to lower spiral spring, 
thence around coil B in same direction as around A, thence 
through a resistance coil and out. 



\NT* 




i 




y b 


c 


^m. 


A 




i"\ \ 

1 ir N * ■'' 


^> 




\ Y * 

1 




i 

S 

Fig. 226. 



The current flowing as shown by the arrows in Fig. 226, the 
field of the fixed coils will be in the direction SN, that of the 
movable coil will be in the direction C and, in accordance with 
Maxwell's law, the needle will move in a clockwise direction. 
When the current reverses its direction both fields are also reversed 
and the tendency is still for the needle to turn in a clockwise 
direction, hence this instrument can be used for both alternating 
and direct currents. 

When the movable, coil has turned until it is at right angles to 
the outer coils the deflecting force is of maximum effect. The 
graduations of the center of the scale are therefore more widely 
spaced than those towards the extremities. 



ELECTRO-MAGNETICS. 



371 



The movable coil turning in a weaker field than in the D. C. 
instruments, the damping effect is much less. To check the 
oscillations of the needle and bring it more quickly to rest, there 
is near the bottom of the coil shaft a circular plate D (Fig. 225) 
against which a light spring brake can be made to press. 

471. The Thomson Inclined Coil Instruments. — These are 
primarily intended for alternating currents and in principle do not 
differ greatly from the one just described, that is there is a movable 
inner coil which rotates in the field of the fixed outer coil. 



(*-- 




u-^- 



Fig. 227. 



Figure 227 represents diagrammatically one of these instru- 
ments, a voltmeter with edgewise scale. The fixed coil A makes 
an angle of 45° with the horizontal base of the instrument. Rotat- 
ing vertically through the center of this coil is the shaft which 
carries the two non-magnetic (phosphor bronze) spiral control 
springs, the needle, the movable coil B and a crescent -shaped 
aluminum disc D. The plane of the rotating coil makes an angle 



372 



ELEMENTS OF ELECTRICITY. 



of 45° with the base of the instrument and is also placed askew 
to the plane of the fixed coil. The current enters at C, flows 
around A in the direction shown by the arrow, thence to the upper 
spiral spring, thence around the coil B in the direction shown, 
thence to the second spiral spring and out through a resistance 
coil. According to Maxwell's law, the rotating coil tends to turn 
until its axis is parallel to that of the fixed coil and the needle 
travels across the scale to the right. 




Fig. 228. 

The inclined coil ammeters differ from the voltmeters just 
described in having no rotating coil but in its place a vane or flat 
sheet of soft iron V (Fig. 228) mounted upon the axis at the same 
angle as that made by the axis of the rotating coil in the voltmeter. 
When a current flows through the fixed coil, the vane tends to 
turn to the position V parallel to the lines of force through the 
fixed coil (Par. 143). 




Fig. 229. 



In the switchboard instruments of this type, damping is effected 
by the aluminum crescent D in Fig. 227 turning between the jaws 



ELECTRO-MAGNETICS. 



373 



of two jew's-harp shaped permanent horseshoe magnets as shown 
in Fig. 229. In the portable instruments a friction brake or air 
vane is used. 

472. Use of Transformers with A. C. Instruments. — Alternating 
current ammeters, due to the effects of self-induction in the coils, 




Fig. 230. 

do not work satisfactorily with shunts and if the current to be 
measured is of such size that in a D. C. instrument a shunt would 
be used, the current through the ammeter is stepped down by 
means of a series transformer as shown in Fig. 230. 

On the other hand, if the pressure in an alternating current circuit 
exceeds about 1000 volts, it is not considered safe to bring this 



VOLTMETER 




Fig. 231. 

voltage direct to a voltmeter and it is stepped down by a potential 
transformer as shown in Fig. 231. These instruments are, of 
course, graduated to read the current or the voltage in the primary 
circuit. 



374 ELEMENTS OF ELECTRICITY. 

473. Millivoltmeters. — If there be constructed an instrument 
like the voltmeter described in Par. 468 but of very much less 
internal resistance (10 instead of 1700 ohms) a slight difference 
of potential between its terminals will drive enough current 
through the coil to move the needle over an extended portion of 
the scale. The scale can therefore be graduated to show much 
smaller fractions of a volt than is possible in an ordinary volt- 
meter. Such an instrument reading to thousandths of a volt is 
called a millivoltmeter. 

474. Millivoltmeters as Ammeters. — Suppose a millivoltmeter 
to be connected to the extremities of a shunt AB as shown in 
Fig. 232. Suppose it has a scale reading to 300 millivolts and that 
its resistance, including that of the leads which accompany it, is 




Fig. 232. 

10 ohms. A difference of potential between AB of three-tenths 
of a volt will throw the needle entirely across the scale. In this 
case the current through the instrument is from Ohm's law 

_ = ^- = .03 ampere. Suppose a current of 300 amperes to be 
ti 1U 

flowing in the main circuit. At A it divides inversely proportional 

to the resistances of the shunt AB and of the instrument and its 

leads. If the resistance of AB be made -ghfo ohm, then 299.97 

amperes will flow through AB and .03 ampere through the 

instrument and the needle will move entirely across the scale. 

The divisions on the scale will therefore correspond to the amperes 

in the main circuit. 

If the resistance of AB be made ¥ VV ohm, then 30 amperes in 

the main circuit will cause the needle to move entirely across the 

scale and the scale divisions will each correspond to one-tenth 

of an ampere. 



ELECTRO-MAGNETICS. 



375 




Finally, if the resistance of A B be made £$ ohm, the scale 
divisions will correspond to one-hundredth of an ampere in the 
main circuit. 

It is therefore possible, by employing a shunt, to use a milli- 
voltmeter as an ammeter. 

475. Millivoltmeter Shunt. — Instead of separate shunts as 
described above, several are usually assembled in one case as 

represented in Fig. 233. The current r 

to be measured is always brought in 
at the upper right hand post and 
leaves by one of the others in the 
upper row. The millivoltmeter is 
connected with the corresponding 
posts in the lower row. The circuits 
are as shown in the figure which repre- 
sents connections made to read a cur- 
rent of a maximum of 1.5 amperes. 
The current in the case represented 
enters at A and leaves at B. AC is a 
heavy copper bar. D, D', D" repre- 
sent diagrammatically strips of resist- 
ance alloy. The numbers on the 
binding posts indicate the number of 
amperes to produce a total scale deflection of the needle when 
connection is made at the corresponding post. These shunts and 
their leads must be used with the particular instrument for which 
they are constructed. 




MILLIVOLTMETER 

Fig. 233. 



376 ELEMENTS OF ELECTRICITY. 



CHAPTER 35. 

HEATING EFFECT OF ELECTRIC CURRENT. 

476. Work Done by Electric Current. — To produce an electric 
current, an expenditure of energy or a performance of work is 
required. According to the fundamental principle of mechanics, 
this energy is not lost but only transmuted and must be given back 
in one form or another by the current. In a cell, for instance, there 
is an expenditure of chemical energy which results in moving Q 
units of electricity through a difference of potential V. The work 
done is therefore W=QV (Par. 72). Since there is no current 
unless there be a complete circuit, each of these Q units of elec- 
tricity must return to its starting point and in doing so passes 
back through the same difference of potential through which it 
was moved, or gives back the energy expended upon it in the first 
place. A current flowing in a circuit must, therefore, perform 
work of some kind, (a) In Par. 215 we saw that a current always 
heats the conductor through which it flows, (b) It may, in 
addition, perform electrolytic (chemical) work, or (c) it may, 
through the medium of machinery, do mechanical work, or finally, 
(d) it may do magnetic work. Energy is also expended by the 
current in establishing a magnetic field about the conductor, but 
this energy need not be considered for it is restored when the 
circuit is broken. If the current performs neither chemical, nor 
mechanical, nor magnetic work, then its entire energy is spent in 
heating the circuit. 

We shall now examine into this heating effect of the current. 

477. Determination of Laws of Heating Effect. — An experi- 
mental determination of the laws governing the heating effect of 
a current was made by Joule with an apparatus similar to that 
shown in Fig. 234. Through the cork of a wide-mouthed glass 
jar containing turpentine, or some similar non-conducting liquid, 
were run two heavy wires and a thermometer, T, all of which 
dipped below the surface of the liquid. Between the ends A and B 
of the large wires, there was connected a slender bare wire of 



ELECTRO-MAGNETICS. 



377 



known resistance, preferably of manganin (Par. 289). The jar 
was then connected in series with a battery, a key and an ammeter. 
Upon closing the key, the current flowed through the circuit and 
heated the small wire, which, in turn, heated the turpentine. The 
strength of the current was read from the ammeter. The increase 
in temperature of the turpentine was determined by the thermom- 
eter, whence, knowing its weight and its specific heat, the number 
of heat units gained could be determined. The length of time 
that the current flowed was also measured. As a result of this 




Fig. 234. 

experiment, Joule found that the amount of heat produced varied 
(a) as the square of the current, (b) as the resistance of the con- 
ductor and (c) as the length of time during which the current 
flowed. 

478. The Joule. — Representing by H the quantity of heat 
produced, Joule's results may be given mathematical expression 
as follows: 

H = PRt 

If in this expression / be one ampere, R be one ohm, and / be 
one second, we have H = 1. This electric unit of heat, the quant it y 
of heat produced by a current of one ampere flowing for one 
second through a resistance of one ohm, has been named the joule. 
It is, however, a redundant unit since we already have in the 
C. G. S. system the small calorie, the amount of heat required to 



378 ELEMENTS OF ELECTRICITY. 

raise one gram of water through one degree Centigrade (Par. 11). 
The joule is a shade less than one-quarter of a calorie. One joule 
is .24 of a calorie and hence one calorie is 4.2 joules. If, therefore, 
H represents the number of calories produced, Joule's law becomes 
H = PRtx0.2A 

479. Theoretical Deduction of Joule's Law. — Joule's law, as 
given in the preceding paragraph, may also be deduced from 
theoretical considerations. Thus, suppose a current of strength I 
is flowing through a simple conductor whose resistance is R. The 
difference of potential between the ends of this conductor is IR 
(Par. 298), and is measured by the work done in moving a unit 
quantity of electricity from one point to the other (Par. 72). If 
the current flows for i seconds, the total quantity conveyed 
between the two points is Q = It, therefore, the total work done 
is IR X It, or PRt, this energy being spent solely in heating the 
conductor. To reduce this to ergs, / and R must be expressed in 
absolute units. Since one ampere = 1(H absolute units of current 
and one ohm = 10 9 absolute units of resistance (Par. 427), we have 
the total energy expended = PRt X 10 7 ergs. In Par. 11 it was 
shown that the small calorie is equivalent to 4.2 XlO 7 ergs. To 
reduce the above expression to calories, we must, therefore, 
divide it by this number, hence 

H = (PRt XlO 7 ) -=- (4.2 XlO 7 ) = PRt/4,.2 = PRt X0.24 
which is the same as the expression in the preceding paragraph. 

480. Electric Heating of Wires. — When a current flows through 
a wire, the wire is heated. The heat generated in the wire is con- 
veyed away, mainly by radiation and convection. The rate at 
which this heat is dissipated increases as the temperature of the 
wire exceeds that of the surrounding medium. The temperature 
of the wire continues to rise until the loss of heat by radiation, etc., 
exactly balances the amount generated by the current. Reflection 
will show that since the heated air in a room ascends, a wire upon 
the ceiling will radiate its heat more slowly than if lower down, 
also, since the insulation upon a wire hinders the escape of the 
heat, the temperature of an insulated wire carrying a current will 
exceed that of the same sized bare wire. If the escape of heat be 
still further impeded by enclosing the wire in a wooden moulding, 
as is sometimes done, its temperature may reach a point where 



ELECTRO-MAGNETICS. 379 

the insulation becomes charred or even where the woodwork is 
set on fire. For this reason, most insurance companies forbid 
the use of these wooden ceiling strips and specify that wiring 
must either be exposed or enclosed in non-combustible conduits, 
and must be so proportioned that its temperature shall never 
exceed a certain allowable maximum. 

481. Calculation of Temperature. — The dissipation of heat 
by a wire varies with the material of which the wire is composed 
and with the nature of its surface, with the extent of this surface, 
with the excess of its temperature over that of the surrounding 
medium and with the nature of this medium. If, when its tem- 
perature is 1° C above that of the surrounding medium it emits e 
calories per second per square centimeter of surface, it will emit 
Te calories per square centimeter per second when its temperature 
is T° C above. If its length be I centimeters and its diameter be d 
centimeters, its surface is irdl square centimeters and its emission 
per second is Terdl calories. During this time, the calories 
generated per second by the current are I 2 /? X 0.24, hence when 
the temperature becomes constant, 

Tewdl = PRx0.24: 

Substituting for R its value (Par. 285) 

I.P 



iird 2 



I=d* 



and solving for I, we have 

T.e.r 2 



,96 X p, 

Applying this to wires of the same material, p is constant, and 
if the wires attain the same temperature, T is constant, hence, 
the current to raise these wires to the same temperature varies 
as the square root of the cube of the diameter of the wires. This 
formula enables us to calculate the size of the fuse wires (Par. 306) 
which will melt when the current reaches a certain maximum. If 
the fuse wire be of tin, its specific resistance p is 13x10-° ohms, 
and e is about .00025. Its melting point being 230° C, T is 230 
minus the temperature (Centigrade) of the surrounding air. 

482. Localizing the Heating Effect of a Current.— If a current 
passes through two portions of a circuit, each of the same resist- 
ance, the amount of heat developed in each will be the same. If 



380 ELEMENTS, OF ELECTRICITY. 

one of these portions be a large wire, several hundred yards long, 
and the other be a small wire, only a few inches in length, the heat 
will still be the same in amount but in the case of the large wire 
it will be distributed over its entire length and, on account of the 
great radiating surface, there will be no perceptible rise in tem- 
perature. On the other hand, the heat is concentrated in the 
small wire, which can not dispose of it by radiation, and the tem- 
perature of the small wire therefore rises. Such is the principle 
upon which the employment of electricity for heating and for 
lighting is based. The current is brought to the required spot 
through wires of but little resistance and is then passed through 
a short length of high resistance, the development of heat being 
thereby localized. If the portion of the circuit is to be heated to 
incandescence, as for example the filament in an incandescent 
lamp, its length must be short and its resistance high. If it is 
merely to be warmed, its length must be greater and its resistance 
less. The following examples will make this clear. 

483. Electric Fuzes. — Electric fuzes are of many kinds. Fig. 
235 represents in section an ordinary blasting fuze, which is also 
variously designated as a primer, a cap, or a detonator. It con- 
sists of a copper case A, which contains the explosive, usually 



■.■.±////;////m2777A 



//. :. ■.■W////////7?r77T7\ 

k^:-r'r:r^^.-,V//////////JJ7^J 



Fig. 235. 

mercuric fulminate, and which is closed by a plug of wood, or wax, 
or sulphur or some similar cementing material. Through this plug 
pass the lead wires which come of various lengths to suit the 
depth of the drill holes in which the blast is to be fired. The inner 
ends of the lead wires are connected by a fine platinum "bridge" B, 
about .001 inch in diameter and one quarter of an inch long. 
About this bridge there is usually wrapped a wisp of gun-cotton. 
The passage of the current heats the platinum bridge and ignites 
the gun-cotton; this, in turn, ignites the fulminate and causes the 
main charge to explode. These fuzes afford the simplest and 
safest method of firing high explosives, and the only certain 
method of blasting under water and of causing a number of charges 
to explode simultaneously. They are fired from a safe distance, 



ELECTRO-MAGNETICS. 38 1 

the current usually being supplied from a hand magneto, although 
it may be furnished by a battery or taken from any other con- 
venient source. In the military service, they are used to explode 
submarine mines and to fire heavy artillery. For this latter use 
they are charged with black powder instead of with the fulminate. 

484. Electric Welding. — If two metal bars connected to the 
terminals of a generator be touched together, the current flowing 
through the resistance along the surface of contact will cause the 
local production of great heat. Such is the principle of the 
electric welding process devised by Elihu Thomson. The bars to 
be welded are brought together, the necessary current is turned 
on and in a very short time the metal softens. If now the bars 
be pressed together, a weld results. In this manner steel axles 
two inches square are joined in a little over a minute and a half. 

Alternating current is used almost exclusively. It was shown 
above (Par. 477) that the heating effect varies as the square of 
the current. By a simple step down transformer (Par. 431) an 
alternating current may be transformed into another whose 
voltage is low but whose amperage is great. Thus, in welding the 
rails of trolley lines, the current is taken from the line itself but 
is transformed down, currents as great as 25,000 amperes being 
employed, and the rails in the mean time being squeezed together 
with a pressure of thirty-five tons. 

485. The Electric Arc. — If the wires attached to the terminals 
of a battery or of a generator be touched together, completing the 
circuit, there will be a rush of current which, on account of the 
localized resistance, will, as we have just seen (Par. 484), develop 
great heat at the point of contact. If the wires be now separated 
about an eighth of an inch and if the E. M. F. between them be 
not less than about forty volts, the current will continue to flow, 
being conveyed by the vapor of the metal volatilized by the intense 
heat, and brilliant light will be emitted by the glowing ends of 
the wires and by the incandescent vapor between. This will 
continue for only a few seconds for the ends of the wires will 
rapidly melt off. If the terminal wires be attached to carbon 
rods which are then touched together and separated, the same 
brilliant light will be produced but in this case it will last much 
longer since the carbon is infusible. The flame, or rather the 
stream of incandescent vapor between the carbons, is really a 



382 ELEMENTS OF ELECTRICITY. 

flexible conductor composed of volatilized carbon and has the prop- 
erties of any other conductor carrying a current. For instance, 
it is surrounded by a magnetic field of its own and if placed in 
another magnetic field will tend to move off to one side (Par. 356). 
Because of the interaction of its field with that of the earth, it is 
generally somewhat curved, and on this account it was named the 
electric arc. If the field be strong enough, the arc may be pushed 
so far to one side as to be extinguished. A form of apparatus 
utilizing this principle to prevent accidental arcs when switches 
are opened is called a "magnetic blow-out." 

As long as the arc is maintained, the carbons consume away 
slowly but at different rates, the positive carbon wasting much 
more rapidly than the negative. The tip of the positive carbon 
becomes hollowed out into a little pit, called the crater; on the 
other hand, the tip of the negative carbon seems to receive the 
particles torn away from the positive carbon and assumes a rather 
pointed outline. 

The chief source of the light of the arc is the crater of the 
positive carbon, the arc itself emitting but little. The maximum 
temperature, however, exists in the arc. This temperature, the 
highest yet attained, is said to be about 3500° C, or twice that 
required to fuse platinum. In this arc the most infusible sub- 
stances are promptly melted and even vaporized. 

486. The Electric Furnace. — Although the light and the intense 
heat produced by the electric arc have been known for over one 
hundred years, it was not until the development within the last 
thirty years of machines for supplying continuously the required 
current that the use of the arc for illuminating purposes became 
commercially practicable, and its utilization on a large scale as a 
source of heat dates from the still more recent development of 
such great sources of power as Niagara Falls. 

Electric furnaces may be divided into two general classes ac- 
cording as the body to be heated is or is not a conductor. If it be 
not a conductor, it must either be placed beneath the arc, the 
heat of which is both radiated and reflected down upon it, or it 
must be intimately mixed with powdered carbon or other conduct- 
ing substance, the passage of the current through which produces 
enough heat to raise the temperature of the body to the required 
point. If it be a conductor, it may be made one electrode of an 
immense arc and be heated both by the heat radiated from the 



ELECTRO-MAGNETICS. 



383 



remaining electrode and by that produced by the passage of the 
current, or it may be heated by the passage of the current alone. 
Of this last class there are two subdivisions according as the cur- 
rent is conveyed directly through the body or is produced in it 
by induction. 

The intense heat of the electric furnace, 3500° C or more, has 
made it possible to fuse silica and to produce therefrom utensils 
of great use in the laboratory; has permitted the reduction of the 
most refractory ores, notably those of aluminum; has enabled 
the chemist to manufacture graphite, silicon, etc.; and finally has 
led to the production of chemical compounds hitherto unknown. 

487. Moissan's Furnace. — One of the earliest electric furnaces 
was that devised by Moissan. It is shown in section in Fig. 236 




Fig. 236. 

and consists of a chamber scooped in a block of lime and covered 
by a lid made from a second block. Lime is used since when either 
hot or cold it does not conduct appreciably. The carbons enter 
through grooves on opposite sides. The body to be heated is 
placed in the cavity in the lower block and the heat produced by 
the arc is reflected down upon it, that is, the furnace is in principle 
a reverberatory furnace. 

Furnaces of this kind can not be made on a large scale. They 
are quite small and are used for fusing small amounts of refractory 
substances, as in the production of artificial gems. 

488. Manufacture of Carborundum. — In 1890 Acheson made 
in a small electric furnace a crystalline substance which he sup- 
posed to be a compound of carbon and corundum, or emery, and 
he accordingly named it carborundum. It is now known to be 
the carbide of silicon, or SiC. It is of great hardness and has come 
into extensive use as an abrasive, displacing emery in the various 
wheels, grindstones, whetstones, polishing cloths and powders. 



384 



ELEMENTS OF ELECTRICITY. 



It is made on a large scale at Niagara Falls. The furnaces, built 
of brick without mortar, are some fifteen feet long by seven feet 
wide and high. At each end (Fig. 237) there are built into the 
wall heavy copper terminals to each of which are attached the 
electrodes proper, sixty carbon rods, three inches in diameter and 
two feet long. These electrodes are connected by a core of crushed 
coke about nine feet long and two feet in diameter. Around this 
core there is packed about ten tons of an intimate mixture of 
34% coke, 54% sand, 10% sawdust, and 2% salt. The salt acts 
as a flux; the sawdust keeps the mass porous. An alternating 
current of 4000 amperes at 185 volts is turned on. This, as will 




be shown in the next chapter, represents about 1000 horsepower. 
In a short while a large amount of carbon monoxide is produced 
and burns as it emerges from the crevices between the bricks. In 
twelve hours the furnace becomes red hot but the current continues 
to flow for twenty-four hours before it is turned off. When it has 
cooled sufficiently the furnace is dismantled. The interior core 
of coke is found to be converted into graphite. This is surrounded 
by a sixteen inch layer of iridescent purplish crystals of carbo- 
rundum. Outside of this layer there are slag-like clinkers. 

In a somewhat similar manner calcium carbide, CaC 2 , is made 
by heating a mixture of lime and powdered coke, the reaction 
being 

CaO+3C = CaC 2 + CO 

Calcium carbide is used for the production of acetylene gas for 
illuminating purposes. 

489. Manufacture of Aluminum. — Although very widely dis- 
tributed, the ores of aluminum are most refractory and until 
recently their reduction was one of the difficult processes in 
metallurgy. The metal is now obtained from bauxite, a mineral 
containing over sixty per cent of aluminum oxide, A1 2 3 . Alone 



ELECTRO-MAGNETICS. 



385 



this is practically infusible but dissolves readily in fused cryolite, 
a double fluoride of aluminum and sodium. The current is passed 
through this fused mass, aluminum is released at the cathode and 
oxygen at the anode. The aluminum being liquid settles to the 
bottom and is drawn off from time to time, fresh supplies of 
bauxite being continually added. The cryolite is not affected. 
The action in this case being electrolytic as well as thermal, 
direct current must be used. Aluminum which ten years ago sold for 
eight dollars a pound can now be produced with profit at twenty- 
five cents. 

490. Electric Iron Furnaces. — There is an increasing use of 
electric furnaces for the treatment of pig iron by a process similar 
to the ordinary open-hearth process. The fused metal is one of 
the electrodes, the other consists of large carbons which penetrate 
the dome of the furnace. The arc plays between these carbons 
and the metal beneath. Suitable linings are used and the proper 
ingredients are added to the molten metal to remove the sulphur, 
phosphorus and other objectionable substances. Such furnaces 
are now made of a capacity of fifteen tons. 




Fig. 238. 



491. The Induction Furnace. — The induction furnace, recently 
introduced for the manufacture of high-grade steel, is a special 
application of the principle of the transformer. It is shown dia- 
grammatically in Fig. 238. P is the primary and S is an annular 
trough of non-conducting fire-brick. Into this trough is placed 
the metal which is to be treated and this mass of steel constitutes 



386 ELEMENTS OF ELECTRICITY. 

a short-circuited secondary of a single turn. The alternating cur- 
rent in P is stepped down in £ to a current of large amperage 
sufficient to bring the steel to a molten state. At the proper time 
the required amount of spiegeleisen or other material is added. 
These furnaces have been made large enough to handle ten tons 
of steel at a charge. 



ELECTRO-MAGNETICS. 387 



CHAPTER 36. 

ELECTRIC POWER. 

492. Power Defined. — If a certain hoisting engine raises a 
weight from the ground to the top of a building in two minutes, 
and a second engine raises the same weight the same height in one 
minute, the work in each case is the same but the second engine 
does its work twice as rapidly as the first and is therefore said to 
be twice as powerful. Power may be defined as the rate of doing 
work. It would ordinarily, therefore, be measured in foot-pounds 
per second. 

493. Horse-Power. — About one hundred and fifty years ago, 
the mine owners in Cornwall employed horses to operate the pumps 
which kept their mines free from water. As the mines sunk deeper, 
the difficulty and expense of removing the water increased so that 
many were abandoned as no longer profitable. It was at this 
time that Watt perfected his steam engine and began to introduce 
it in the mines. The miners knew how many horses were required 
to lift so much water but had no notion of the capabilities of the 
new-fangled engine; they therefore required that before purchas- 
ing an engine they should be told how many horses it could sup- 
plant. In order to be able to furnish this information, Watt 
carried out a series of tests with the powerful horses used in the 
London breweries, as a result of which he concluded that such a 
horse working eight hours a day could perform work at a rate 
equivalent to raising 33,000 pounds one foot per minute. This 
figure has ever since been accepted as the measure of a horse-power. 
The unit of time is, however, commonly taken as one second, the 
corresponding foot-pounds being 550. 

In electrical measurements, it is desirable to express this in 
absolute units. Remembering that the pound is about 445,000 
dynes (Par. 11), and that the foot = 30.48 centimeters, the horse- 
power is in round numbers 7,460,000,000 (or 746 XlO 7 ) ergs per 
second. 

494. Expression for Electric Power. — There are a number of 
ways in which an expression for electric power may be deduced. 



388 ELEMENTS OF ELECTRICITY. 

It is superfluous to say that in every case the results must be the 
same, yet, several of these methods will now be explained, for each 
presents the matter from a slightly different view-point and the 
student will thus get a broader grasp of the subject. We shall 
begin with the simplest. 

(a) In Par. 477 we saw that the heat developed by a current of 
strength I flowing for t seconds through a resistance R is PRt. 
This represents energy expended, or work, and if divided by t it 
will give the rate at which the work is done, or the power (Par. 
492). Hence, the power developed by a current I in heating a 
resistance R is PR. 

This last expression may be factored as follows: PR = IxIR. 
But IR is the drop of potential E between the two points A and B 
(Fig. 234), hence for PR we may write IE, or the power expended 
in heating any portion of an electric circuit is measured by the 
product of the current flowing in the circuit by the difference in 
potential between the ends of the portion. 

(b) In Par. 358 it was proven that the work done by a current 
I flowing around a coil is, IN, N being the change in the number 
of lines of force embraced by the coil. If this work be done in time 
t, the power = IN/t. But (Par. 425) N/t = E, and the foregoing 
expression also reduces to IE, or, as above, the power developed in 
a coil, a portion of a circuit, is measured by the product of the cur- 
rent flowing through the circuit by the difference in potential 
between the ends of the coil. In this case, the heating effect is 
not considered specifically. 

(c) Finally, taking the most general case of a portion of a circuit 
of any shape whatsoever, and placing no restriction upon the 
nature of the work performed by the current, if E be the difference 
of potential between the ends of the portion and if during the time 
under consideration Q units are transferred around the circuit, the 
work done in the portion is QE (Par. 72). But Q = lxt, hence the 
work is 7. t. E. Dividing this by t to obtain the power, we again 
arrive at IE, or, in general, the power expended in any portion of 
an electric circuit is measured by the product of the current by the 
difference in potential between the ends of the portion. 

495. Development of Power in a Battery. — Since the source of 
the energy developed in a single cell is the chemical action result- 
ing in the consumption of the zinc by the acid (Par. 192), no matter 



ELECTRO-MAGNETICS. 389 

how a battery may be grouped, if the same amount of zinc be con- 
sumed in the same time, the same power is developed. This may 
be illustrated as follows: Suppose N cells, each of an E. M. F. of 
e volts and an internal resistance of r ohms be grouped in series 
with an external circuit of negligible resistance. The E. M. F. of 
the battery is Ne, the current is Ne/ Nr = e/r, and if z be the zinc 
consumed in one cell per second, the total amount consumed per 
second is Nz. 

If these same cells be grouped in parallel, the E. M. F. of the 
battery is e, the current through each cell is e/r, the total current 
is Ne/r and the total consumption of zinc per second is again Nz. 
The power developed in the two groupings should therefore be the 
same. In the first case it is NeXe/r or Ne 2 /r; in the second case 
it is e X Ne/r or again Ne 2 /r. 

496. Units of Electrical Power. — From Par. 494 the expression 
for electrical power is 

P = IE 

If in this, I be one absolute unit of current and E be one absolute 
unit of E. M. F., P becomes one absolute unit of electric power. 
This unit has received no name but represents the expenditure of 
energy at the rate of one erg per second. 

If in the same expression, we make / one ampere and E one 
volt, we again have P = 1. This unit, the practical unit of electric 
power, is called the watt. Since the ampere is 10 -1 absolute units 
of current and the volt is 10 8 absolute units of E. M. F. (Par. 427), 
the watt= IE = 10 -1 X 10 8 = 10 7 absolute units of power, or ten 
million ergs per second. 

We saw in Par. 493 that the horse-power was 746 XlO 7 ergs per 
second. The horse-power is therefore 746 watts. The commercial 
unit of electric power is the kilowatt, or one thousand watts. The 
kilowatt is 1000/746, or just about 1\ horse-power. The com- 
mercial unit of electric work, the unit by which it is bought and 
sold, is the kilowatt-hour. 

497. Measurement of Electric Power. — Since the power ex- 
pended between two points in an electric circuit is measured by the 
product of the current by the difference in potential between the 
two points, we may measure the current by an ammeter, and 
the difference of potential by a voltmeter, and by multiplication 
obtain the watts. As an illustration, suppose we wish to determine 



390 



ELEMENTS OF ELECTRICITY 



the consumption of power in the 16 candle-power, 100 volt lamp, 
AB, Fig. 239. Connections are made as shown. The ammeter 
reads the current / flowing through AB, and the voltmeter reads 
the difference of potential E between A and B. The product of 
these two readings gives the watts consumed. If, for example, 
the current be one-half ampere and the difference of potential 
between A and B be 100 volts, the power is 50 watts. It requires, 




Fig. 239. 

therefore, a kilowatt to run 20 such lamps, or about one horse- 
power to run 15. 

If, in the above example, the ammeter be read while the volt- 
meter is connected up, a slight error will be committed, for exami- 
nation of the figure will show that the ammeter reads not the 
current through the lamp but the sum of the currents through 
both the lamp and the voltmeter. If the resistance of the volt- 
meter be 15,000 ohms (Par. 458), the current through it is t Mtfo 
or T io ampere. The current through the lamp is therefore really 
\ — T ^o = t¥o ampere, and the power consumed in the lamp is 
100 X t 7 /o = 49^ watts instead of 50, indicating an error of l£ per 
cent. This may be reduced by connecting the voltmeter, as shown 
by the dotted line D, in shunt with both the lamp and the am- 
meter, or by reading the ammeter before the voltmeter circuit is 
closed. In a similar manner it may be shown that if the current 
be large and the difference of potential between A and B be small, 
the connection as shown in the figure is the best. 

The determination of power from the reading of two separate 
instruments does not give correct results when applied to alternat- 
ing current circuits. This fact cannot be explained until the 
subject of alternating currents is reached. 



ELECTRO-MAGNETICS. 



391 



498. Measurement of Power by Electro-Dynamometer. — By 

making a slight change in the connections of an electro-dynamom- 
eter, it is possible to use that instrument to measure electric 
power. For example, suppose we wish to measure the power ex- 
pended in an incandescent lamp. Connections are made as shown 




Fig. 240 



diagrammatically in Fig. 240. F represents the heavy wire fixed- 
coil of a Siemen's electro-dynamometer (see Fig. 171). The end 
of this coil connected to the terminal A is left undisturbed. The 
other end, which was fastened to the metal bracket at D, is discon- 
nected and attached to G, one terminal of the lamp. The main 
current now enters at H, passes through the lamp and the coil F 
and out by A. A current is shunted off at H, passes through a 
resistance R of several thousand ohms, thence to the terminal C, 
thence around the movable coil M to the bracket D and finally 
reunites with the main current at G. 

In Par. 383 it was shown that the force exerted between the two 
coils carrying currents is f=K 1 1' 

K being a constant and / 
and I' being the currents in the respective coils. If E be the dif- 
ference of potential between H and G, and if R be the resistance 
of the shunt circuit HRCMDG, then the current through the 
movable coil is I' = E/R. Substituting this for V in the expres- 
sion above, we have rr 



W E) 



whence, since K and R are 



392 



ELEMENTS OF ELECTRICITY 



constants, we see that the force exerted between the two coils of 
the instrument is proportional to IE, the watts consumed between 
H and G. In the same paragraph it is shown that this force is 
proportional to the angle of torsion, that is, to the angle through 
which the milled head of the dynamometer is turned in order to 
bring the pointer of the movable coil back to the zero, whence the 
wattage between the points H and G is also proportional to this 
angle. 

As pointed out in Par. 497, an error is committed in this meas- 
urement unless the shunt current (the voltage current) be so small 
as to be negligible. On this account, the resistance R is made very 
large. 

499. Indicating Wattmeter. — Instruments from which may be 
read direct the power developed between two points in a circuit 




are called wattmeters. They are of two general classes, the first 
giving the value of the power at any instant and called indicating 
wattmeters; the second summing up or integrating these instan- 
taneous values and called integrating wattmeters. 

Indicating wattmeters operate on the principle of the electro- 
dynamometer described in the preceding paragraph, but are usual- 
ly so arranged as to avoid the errors pointed out in Par. 497. Fig. 
241 represents the external appearance of the Weston wattmeter. 
Across the top there are three terminals, the outer ones being used 



ELECTRO-MAGNETICS. 



393 



for the voltage current and one of them being marked + . The 
central terminal is used in a certain process of calibration, not 
necessary to describe here. On the left side are the two terminals 
for the main current, one of these also being marked +. At the 
bottom is a button switch which closes the voltage circuit. This 
instrument may be used with either direct or alternating currents. 
When in use, if the main current be brought in at the plus terminal, 
the voltage current must enter by the plus terminal of the top 
row; if the main current be brought in at the negative terminal 
the voltage current must enter by the negative terminal of the 
top row. 

The internal arrangement of the instrument is quite similar to 
that of the D. C. A. C. voltmeter as described and figured in Par. 
470. Fig. 242 represents diagrammatically the connections made 




ift^ss 



Fig. 242. 

to read the power consumed in two incandescent lamps in series. 
The main current enters at A, passes around the two fixed coils 
in the direction shown by the heavy arrows, and leaves by B. It 
does not pass through the movable coil. The voltage current is 
shunted off at C, enters at D, passes through the large resistance 
R, which is wrapped so as to be free from inductance, thence to 
the movable coil around which it flows as shown by the broken 
arrow, then around the fixed coils but opposite in direction to the 
main current, thence out by E, and rejoins the main current at F. 



394 ELEMENTS OF ELECTRICITY. 

The current through the fixed coils, as has already been pointed 
out (Par. 497), is greater than the current through the lamps 
since it consists of that current plus the shunt current. To 
correct for this, the shunt current is carried around the fixed coils 
in opposite direction to and making as many turns as the main 
current. 

500. Integrating Wattmeter. — A consumer of electrical power is 
charged on an equitable basis when he pays in proportion to the 
work performed for him by the current. He must therefore pay, 
not for the power alone, but for the product of the power and the 
time during which it has been supplied, for since power is the 
rate of doing work = w/t (Par. 492), work is equal to power X time. 
Electrical power is therefore sold not by the watt, but by the watt- 
hour, or more usually by the kilowatt-hour (Par. 496). The 
wattmeter described in the preceding paragraph indicates the 
instantaneous values of the power but takes no account of the 
time element. Instruments which sum up the successive amounts 
of work performed by the current are called integrating wattmeters. 
Their principle is simple but can not be fully explained at this 
point. One form consists of a coil which revolves continuously 
as long as the current flows through it, the rate of revolution 
at any instant varying directly with the power, and therefore 
the total number of revolutions varying with the total amount of 
work performed. These revolutions are recorded by an arrange- 
ment like that used in cyclometers but the dials are graduated to 
read kilowatt-hours direct. The instrument is therefore anal- 
ogous to a gas-meter which indicates at any instant the total 
amount of gas which has flowed through it up to that time but 
does not indicate the amount actually flowing through. 

501. Electrical Transmission of Power. — The two prime sources 
of power utilized at present are water and steam. Of these, water 
power is much the cheaper. 

'The difference in level, upon which water power largely depends, 
may be natural, as in the case of falls, or may be artificially 
produced by the erection of dams. In either case, unoccupied 
localities suitable for the development of such power are rapidly 
becoming scarce. In the immediate vicinity of these falls and 
dams, the available sites for power plants are usually restricted. 
By means of shafting, belting, cables, etc., the power developed 



ELECTRO-MAGNETICS. 395 

by these plants may be transmitted a few hundred feet. Beyond 
this limited zone, recourse must be had to steam power. 

In the majority of steam plants, coal is the fuel used and this 
has to be transported from the mines to the plants. On the aver- 
age, the cost of transportation is greater than the cost of the coal 
itself, therefore, steam plants located near the mouth of a coal 
mine have a great advantage over those at a distance. 

From the foregoing, the need of a method of cheap transmission 
of power to a distance is evident. This problem is solved by elec- 
tricity, the mechanical power developed by the plant being trans- 
formed into electrical power, sent out over the line to the desired 
spot and there transformed back into mechanical power. 

502. Considerations Affecting Electrical Transmission of 
Power. — It was shown above (Par. 494) that the electrical power 
between two points in a circuit is measured by IE, the product 
of the current by the difference of potential between the points. 
These two quantities may therefore vary reciprocally and the power 
remain constant. This principle is of the utmost importance in 
the electrical transmission of power. When a current flows through 
a conductor, a portion of the power is spent in heating the con- 
ductor, the power so spent being PR (Par. 494), or varying as the 
square of the current. To avoid this waste, the current should be 
kept as small as possible. From what has been shown above, we 
can reduce the current and still transmit the same power pro- 
vided the voltage is varied inversely with the current. An ex- 
ample will bring this out more clearly. 

Suppose an electric generator operated by a water wheel is pro- 
ducing ten amperes at a pressure of two hundred volts, or develop- 
ing a power of 2000 watts, and is transmitting power over a No. 3, 
B. and S., copper wire to a factory at a distance of five miles. For 
round numbers, the resistance of this wire may be taken as one 
ohm per mile. The PR loss due to the resistance of the wire is 
100 XlO = 1000 watts, that is, fifty per cent of the power generated 
is lost in the wire. If this same generator turned out one ampere 
at a pressure of 2000 volts, it would still develop the same power, 
2000 watts, but in this case the PR loss would be only 10 watts, 
or only one-half of one per cent of the total power. Furthermore, 
if the fifty per cent loss be permissible, a No. 15 wire may be used 
with the 2000 volt current and the loss still be kept within the 
limit. Since the No. 15 wire weighs 52 pounds per mile as com- 



396 ELEMENTS OF ELECTRICITY. 

pared to 838 pounds for the No. 3 wire, there would result a saving 
of 7860 pounds of copper costing about $1000. 

The secret of electrical transmission of power to a distance is 
therefore the employment of high potential currents. As will be 
shown in Part V, high potential alternating currents are much 
more easily generated and transformed up and down than are 
corresponding direct currents, for which reasons, in the transmis- 
sion of power to a distance, alternating currents are used almost 
exclusively. Voltages as high as 20,000 and 30,000 are frequently 
employed, and in a few cases 150,000 has been reached and power 
has been transmitted upwards of three hundred miles. With 
these very high voltages, the difficulty of obtaining proper insu- 
lation for the line increases greatly. The wires must be spaced 
widely apart on the cross arms of the poles and special forms of 
porcelain insulators must be used. In rainy weather, the loss 
from leakage becomes excessive. Finally, the element of danger 
to life assumes serious proportions. 



ELECTRO-MAGNETICS. 397 



CHAPTER 37. 

ELECTRIC LIGHTING. 

503. The Electric Light. — In Chapter 35 we examined the heat- 
ing effect of the electric current. If a body be raised to a suf- 
ficiently high temperature it will emit light. The production of 
light by electricity is therefore only a particular case of heating. 

There are at present three distinct classes of electric lights. 
These are: 

(a) The incandescent lamp. The current is passed through a 
conducting solid which is raised to incandescence. No combustion 
takes place. 

(b) The arc lamp. The current is passed across the gap be- 
tween two electrodes whose tips are thereby heated to incandes- 
cence. A portion of one of the electrodes is volatilized and the 
resulting vapor conducts the current across the gap. Combustion 
takes place, but simply because air cannot be excluded. 

(c) The luminous vapor lamp. The current passed through 
rarefied gases or vapors contained in glass tubes causes these 
vapors to glow. No combustion takes place. 

504. The Incandescent Lamp. — The incandescent lamp does 
not differ in principle from the fuze described in Par. 483. The 
earlier forms consisted of a bare platinum wire which was made 
white-hot by the passage of the current. These failed because the 
platinum was necessarily near its melting point and a slight in- 
crease in the current would cause it to give way; moreover, 
the cost of the platinum was excessive, and for these reasons the 
incandescent lamp did not become a commercial success until the 
development by Edison of the carbon filament. Carbon is infus- 
ible and, although a conductor, is a poor enough conductor to 
permit the filaments to be made of sufficient size for strength and 
yet preserve the resistance required for the development of the 
heating effect. If, however, carbon be heated in the presence of 
oxygen it is soon consumed. The filaments must therefore be 
enclosed in a vacuous glass bulb or with an inert gas. 



398 ELEMENTS OF ELECTRICITY. 

505. The Carbon Filament. — The first successful carbon fila- 
ments were made from bamboo. Later on, they were made from 
a compact paper which was cut into thread-like strips. They have 
also been made from cotton thread. They are now manufactured 
from a pure cotton fibre which is dissolved into a glue-like liquid 
by a solution of zinc chloride. This is forced through small holes 
in a die and emerges in rather soft endless threads, a little over one- 
fiftieth of an inch in diameter, which are caught in a vessel con- 
taining alcohol. The alcohol dehydrates and hardens the threads, 
which are then washed free of the zinc chloride, coiled up and 
dried. They now resemble fiddle strings. These are cut up into 
the proper length, given the required shape by being wrapped 
upon a form and are then embedded in pulverized carbon in a 
covered crucible and carbonized at a high temperature. After 
cooling, they are attached to holders, placed in a vessel in which 
they are surrounded by the vapor of gasoline, and heated white 
hot by a current. This process is called "flashing." The gasoline 
is decomposed and deposits a semi-metallic film of gas coke on the 
filaments. This renders them stronger, more uniform in resistance, 
and of a steely black color. The diameter has now shrunk to .0035 
inch. 

An additional process recently introduced, consists in placing 
the filaments, both before and after flashing, in an electric furnace 
and raising them to a still higher temperature by which they are 
partially graphitized. Filaments so treated are said to be "metal- 
lized," and their light-giving efficiency is much increased. 

506. Manufacture of the Lamps. — The current enters and leaves 
the glass bulb through two wires fused into a small glass tube or 
stem which is inserted into the bulb and fused to it. The portion 
of these "leading-in wires" which passes through the glass of the 
stem (A and B, Fig. 243) must be of platinum. The coefficients 
of expansion of glass and of platinum are about the same and they 
therefore expand and contract together. With other metals, the 
glass would either be cracked by the greater expansion of the wire 
or the vacuum would be destroyed by the shrinking of the metal 
away from the glass. Copper wires are fastened to the outer ends 
of A and B and the filament is attached to the other ends by means 
of a carbon paste. One of the copper wires is soldered to the brass 
shell which carries the screw threads of the lamp base. The bot- 
tom of this shell is closed by a glass or porcelain button in the center 



ELECTRO-MAGNETICS. 399 

of which is a brass contact, pierced with a small hole. The remain- 
ing copper wire is drawn through this hole and soldered to the 
contact. The shell is fastened to the bulb by a cement or by plaster 
of Paris. Lamp sockets are so arranged that when a bulb is 
screwed in, the required connections are made. 

A small tube is left at E. This is now attached to an air pump 
and most of the air is withdrawn from the bulb. When a good 
vacuum has been obtained, a current is sent through the lamp. 
This drives out the gases which have been occluded in the carbon 
filament. The last traces of oxygen are removed by igniting a 
small amount of phosphorus inserted for that purpose at E, and 
E is then sealed by a blow-pipe flame. 




Fig. 243. 

In lamps with long and slender filaments, the filaments are liable 
to be broken by excessive vibration, or when hot may droop, touch 
the bulb and crack it. To remedy this they are often supported 
at their middle point by a short wire, one end of which is fused into 
the tip of the glass stem on the interior of the lamp. Such fila- 
ments are said to be ' 'anchored.' ' 

Incandescent lamps are run at constant voltages. Since the 
heating effect, on which the light-giving effect depends, varies as 
PR = IE (Par. 477), and since E is constant, the lighting effect is 
increased by increasing the current. This is done by decreasing 
the resistance of the lamp, that is, by making the filament shorter 
and stouter. 

507. Recent Incandescent Lamps. — As has just been stated, 
the light-giving effect of an incandescent lamp increases with the 
temperature. It is therefore desirable to heat the filament as 
highly as possible. As the temperature of the ordinary carbon 
filament increases, so does the brilliancy of the light it emits, but 
the life of the lamp is very much shortened thereby and it is not 
found practicable to exceed a temperature of 1350° C. 



400 



ELEMENTS OF ELECTRICITY 



We saw (Par. 504) that in the early lamps attempts were made 
to use platinum filaments. Platinum, which fuses at 1775° C, 
was the most infusible metal which could then be obtained yet 
had to be abandoned because the filaments melted. There are 
known, however, certain rare metals whose fusing points are much 
higher than that of platinum. Among these are osmium, tantalum 
and tungsten, this last fusing at 3200° C. Their rarity, the dif- 
ficulties of their metallurgy, and their consequent cost prohibited 
their use. These metals may now be obtained and are success- 
fully used in incandescent lamps. Their conductivity being so 
much greater than that of carbon, in order to secure the necessary 
resistance they must be drawn into extremely fine wires. When 
they have been drawn down so that they look almost as slender as 
a spider's web, their resistance is still too small and can be in- 




Fig. 244. 

creased only by taking longer portions for filaments, about twenty 
inches on an average. Even with this length, it is stated that as 
many as 20,000 may be made from a single pound of tantalum, and 
this although the specific gravity of tantalum is greater than that 
of lead. To insert these long filaments into the lamp bulb, they 
must be folded back and forth a number of times and having very 
little rigidity when cold and becoming soft when heated, they must 
be supported at several points. . The expansion and contraction of 
a twenty-inch filament, especially if it be attached to supports at 
intermediate points, is very liable to break it, for which reason it 
is found better to cut the. filament into four or five pieces and to 
connect these pieces in series. Even in this case, especial provi- 
sion must be made to allow for the expansion and contraction. 
Fig. 244 shows diagrammatically the arrangement of the filament 
in a tungsten lamp. The leading-in wires pass through a glass 
stem just as in the carbon lamp. To this stem and in prolongation 
of it there is fused a slender glass rod expanded into a button at 



ELECTRO-MAGNETICS. 401 

A and at B, points about two inches apart. Into the button A 
there are fused four V-shaped pieces of wire, the vertices of the V's 
being embedded in the glass so that the free ends radiate like the 
spokes of a wheel. Into the button B there are fused five equi- 
distant straight pieces of wire. These are shorter than the pieces 
in A, but are brought out to the same length by an attached piece 
of the filament wire, this last terminating in a small circular loop. 
A piece of the filament is attached to the terminal C, the free end 
is then threaded through the loop D and brought back and at- 
tached to E. A second piece is attached to F, carried through the 
loop G and fastened to H, and so on around the axis. A develop- 
ment of these connections is shown at the right of Fig. 244, whence 
it is seen that the successive pieces of filament are in series. The 
flexible ends of those arms which radiate from B allow for the ex- 
pansion and contraction of the filaments which they support. 
These lamps produce a very fine white light with a smaller expendi- 
ture of energy than in the case of the carbon lamp. 

508. The Nernst Lamp. — The oxides of certain of the rarer 
metals, yttrium, thorium, zirconium, are infusible and if highly 
heated emit a very bright light. It is on this account that these 
oxides are used in the mantles of the Welsbach burner. When 
cold, they do not conduct electricity but if heated to about 700° C 
they become conductors and if a current be now passed through 
them they may be heated to a point where they glow with great 
brilliancy. This property is utilized in the Nernst lamp. The 
light is emitted from a glower, a little rod of these oxides about 
two centimeters (three-quarters of an inch) long and one millime- 
ter in diameter. The light-giving power of a lamp is increased by 
using more than one glower. The lamp must be provided with 
an auxiliary arrangement by which (a) the glower is heated up to 
the conducting point and (b) the current is then switched from the 
heater to the glower. 

Fig. 245 shows diagrammatically the operation of the lamp. 
A is an armature, bent at an angle and pivoted as shown. Its 
shape causes its lower end to hang out and make contact at C. 
H is the heater, a slender porcelain tube around which is wrapped 
a coil of very fine platinum wire which, for protection, is embedded 
in a white cement paste. M is an electro-magnet with an L-shaped 
core. The current enters at D, travels down A, passes through the 
contact C, around H and out by E, The passage of the current 



402 



ELEMENTS OF ELECTRICITY. 



through H heats it and in less than half a minute the glower G has 
been raised to a conducting temperature. The current entering at 
D may now pass around M, through the resistance B, through G 
and out. M becomes magnetized, the armature A is attracted and 
the contact at C is broken. The full current now passes through G. 
Owing to the method of operation of the current shifter, these 
lamps are restricted to a vertical position. 




Fig. 245. 

As the temperature of G rises, its resistance decreases. This 
would permit a larger current to flow through G and its tempera- 
ture would rise still higher, and so on, until the glower would be 
melted. This rise of current, however, is controlled by the resist- 
ance B, a fine iron wire which, to prevent oxidation, is sealed up in 
a glass tube in an atmosphere of nitrogen. It is adjusted to permit 
the passage of the required current at the voltage for which the 
lamp is intended. The resistance of iron increases rapidly with 
the temperature and an increase of seven per cent in the current 
will double the resistance of B. Variations in the voltage do not, 
therefore, cause proportional variations in the current through the 
lamp. A resistance such as B, which steadies or prevents undue 
fluctuations in the current, is commonly called a "ballasting coir' 
or simply "ballast." 

Since the glower is composed of oxides, it is not necessary to 
seal it up in a bulb. It is, however, usually surrounded by a 
glass globe. Doubtless on account of electrolytic action, the 



ELECTRO-MAGNETICS. 403 

life of a glower is less with direct current than with alternating 
current. 

509. Candle -Power. — Lamps are rated according to the in- 
tensity of the light which they emit under normal conditions, as 
4, 8, 10, 16, 32, 50, and 100 candle-power. The British standard 
candle is defined as a spermaceti candle, seven-eighths of an inch 
in diameter, weighing one-sixth of a pound, and burning at the 
rate of 120 grains per hour. The German standard, the Hefner 
unit, or the hefner, is the light emitted by a lamp of prescribed 
dimensions burning amyl acetate. The hefner is about .88 of a 
candle-power. In actual measurements of candle-power, use is 
made of secondary standards, incandescent lamps whose candle- 
power has been determined by comparison with the primary units. 
The standards in use in this country are determined from the 
hefner. 

In many electric lamps, the light emitted in certain directions 
is greater than that emitted in others. Such lamps are frequently 
rated according to their mean spherical candle-power, that is, the 
candle-power if the total light emitted were spread uniformly over 
the surface of a sphere with the lamp as a center. 

510. Photometry. — Measurement of candle-power is made by 
photometers. Various kinds of these instruments are described in 
detail in the electrical handbooks. In brief, they consist of an 
arrangement by which a beam from the standard falls side by side 
on a screen with a beam from the light being measured. One of 
the lights is shifted back and forth until the illumination on the 
adjoining surfaces is the same. When this equality of illumination 
has been attained, then, since the intensity of illumination varies 
inversely as the square of the distance from the source, the candle- 
power of the lamps are to each other directly as the squares of 
their respective distances from the screen. 

511. Life of Incandescent Lamp. — The life of an ordinary 16 
candle-power incandescent lamp may exceed 2000 hours. How- 
ever, the candle-power of a lamp, although slightly above normal 
for the first fifty hours, decreases steadily thereafter, and it is laid 
down as a rule that the smashing point of the lamp is reached when 
its candle-power has fallen to 80 per cent of its rated value. This, 
on an average, is after about 600 hours' use. The useful life 
depends greatly upon the accuracy with which the voltage is 



404 ELEMENTS OF ELECTRICITY. 

regulated. It is stated that an increase of three per cent in the 
voltage will shorten the life of a lamp one-half. On the other hand, 
a decrease of ten per cent in the voltage reduces the candle-power 
47 per cent. 

512. Efficiency. — The efficiency of an incandescent lamp should 
be measured by the light produced by the expenditure of a certain 
amount of power, that is, by the candle-power per watt. In practice 
however, a custom the reverse of this has arisen and the efficiency 
of a lamp is given by stating the number of watts required to pro- 
duce one candle-power. In this case, the greater the number of 
watts, the less the efficiency of the lamp. The hot resistance of an 
ordinary 110 volt, 16 candle-power lamp is 220 ohms. The current 
through the lamp is therefore one-half ampere, and the power con- 
sumed is 110x1/2 = 55 watts. The wattage per candle-power is 
therefore 55/16 = 3.4. By increasing the voltage, more light is 
produced and the efficiency may be made 2.7 watts per candle- 
power, but in this case the life of the lamp is very much shortened 
(Par. 511). 

The efficiency of the Nernst lamp is 1.75 watts per candle- 
power and that of the tungsten lamp is 1.5 watts or even less. 

513. Control of Light. — An objection to the incandescent lamp 
is that it can not easily be turned down. We shall see later that 
if a large number of closely-grouped lamps, such as are used in 
illuminating the stage of a theatre, be run by alternating cur- 
rent, it is possible to turn them down simultaneously by a simple 
piece of apparatus (Par. 621), but it is not practicable to apply 
this to individual lamps. It is theoretically possible to insert 
in series with a lamp a variable resistance, a rheostat (Par. 302), 
by which the current, and consequently the light, may be con- 
trolled, but the cost and the necessary bulk of such arrangement 
prohibit its use. 

514. Grouping of Incandescent Lamps. — Assuming that in 
transmitting electrical power from the generator to the spot where 
the power is to be used the principles outlined in Par. 502 have 
been observed, in utilizing this power for purposes of illumination, 
the lamps may be grouped either in series or in parallel, though the 
latter arrangement is by far the commoner of the two. Among 
the considerations which lead to the selection of one grouping 
in preference to the other, the principal are the distances by which 



ELECTRO-MAGNETICS. 405 

the individual lamps are separated and the nature of the current, 
whether direct or alternating. 

If the lamps are to be located close together, as in the illumina- 
tion of the rooms of a building, the parallel arrangement should be 
followed. A striking advantage of this arrangement is the in- 
dependence of the several lamps and the automatic adjustment 
of the current to suit the demands made upon it. The following 
will make this clear. 

In Fig. 246, G represents a generator constructed, as will be ex- 
plained in Part V, so as to maintain a constant difference of poten- 




Fig. 246. 

tial between the mains A and B. L represents a number of lamps 
arranged in parallel between these mains. Suppose the resistance 
of a lamp to be 220 ohms, and the difference of potential between 
A and B to be 110 volts. If one lamp be turned on, the current 
through it will be I = E/R = 110/220 = 1/2 ampere. If four lamps 
be turned on, the resistance between A and B is reduced to 220/4 
= 55 ohms and the current is now 110/55=2 amperes, but since 
there are four paths, one-fourth of the total current, or one-half 
ampere, flows through each so that each lamp gets its proper cur- 
rent. So long as the difference of potential between A and B is 
maintained, each lamp when turned on will receive its proper 
current, and whether it be turned off or on will not interfere with 
the remaining lamps. 

There are still other parallel arrangements, such as the three- 
wire system, the five- wire system, etc., in which more than two 
mains are used, but explanation of these is deferred until the 
machines supplying the currents for these systems have been 
described. 

If the lamps are to be widely scattered, as in street illumination, 
they should be arranged in series and supplied by a constant current 
generator. At the Military Academy the roads are lighted b\ 
incandescent lamps, each requiring three amperes at 50 volts, and 
arranged in series, 50 in a circuit. The generator must, therefore, 
supply three amperes at a pressure of 2500 volts. Were these 



406 



ELEMENTS OF ELECTRICITY. 




lamps arranged in parallel, the mains would have to carry, for a 
portion of their length at least, a current of 150 amperes. 

Since the lamps are in series, should one burn out, the remainder 
would ordinarily be extinguished. To avoid 
this, an arrangement shown diagrammatically 
in Fig. 247 is employed. From the lamp socket 
proper there extend downward two brass 
springs C and D, shaped so that they press 
tightly together like a pair of spring tweezers. 
They are kept from actual contact by a thin 
sheet E of mica, or of similar insulating ma- 
terial, which is inserted between them. When 
in position, these upper springs make contact 
with corresponding springs A and B, by which 
the current is brought in and taken out. Should 
the lamp burn out, breaking the circuit, the 
voltage between C and D, which up to this time 
had been 50, immediately mounts to 2500. This 
is sufficient to pierce the sheet of mica E, burn 
Fig. 247. it out, and re-establish the circuit. 

515. The Arc Lamp. — The electric arc was described in Par. 485 
and later its use in the electric furnace was explained. It was also 
pointed out that not until the comparatively recent development 
of machinery for supplying the necessary current did it become 
possible to utilize it. It was discovered by Davy in 1808. By 
means of a battery of 2000 cells and with charcoal electrodes he 
produced an arc four inches long and of very great brilliancy. 
Thirty-five years later Foucault substituted the more compact gas 
coke for the charcoal used by Davy. Carbon is still the principal 
material used, although certain other substances have recently 
been introduced (Par. 523). 

Arc lamps may be grouped in series or in parallel, the same con- 
siderations governing as explained in the preceding paragraph. 
Since they are most largely used for external illumination, and 
also since they require a much larger current than does the incan- 
descent lamp, they are usually arranged in series. 

516. The Carbons. — The carbons for use in the arc lights are 
made with the greatest care. They are made from lampblack, or 
from gas coke, or from a similar coke produced in refining certain 



ELECTRO-MAGNETICS. 407 

petroleum products. These forms of carbon are ground to a very 
fine powder, passed through a bolting cloth like that used in the 
manufacture of flour, and intimately mixed with granulated pitch 
which is warmed enough to cause the ingredients to adhere. The 
mixture is then cooled and again ground to a fine powder and 
passed through the bolting cloth. The resulting meal is formed 
into rods, either by being compressed between steel molds by 
hydraulic pressure or by being forced through a die and emerging 
in a continuous piece which is cut up into the required lengths. 
The rods are then placed in layers in a furnace, the layers being 
separated and covered by sand, and they are then heated and 
maintained at a high temperature for from ten days to two weeks. 
In this process a good many are spoiled by warping. The carbons 
thus prepared are frequently copper-plated. The coating of cop- 
per strengthens the rods, prevents chipping and the formation of 
dust, and adds about one-fifth to the life of the carbon, but its 
main object is to obtain a better electrical contact. The molded 
carbons are the most largely used but, mainly because of the re- 
mains of the web along the sides, they are not exactly cylindrical 
and can not be used in certain forms of arc lamps described later 
(Par. 521). The pressed carbons are perfectly cylindrical and 
when necessary can also be made in the form of a tube for the 
manufacture of cored carbons. The average arc light carbons are 
one-half inch in diameter and vary from six to twelve or more 
inches in length. Their average resistance is 0.15 ohm per foot. 
Carbons for search lights may be as much as two inches in diam- 
eter. 

517. Requirements of Arc Lamp Mechanism. — The mechanism 
of an arc lamp must automatically perform the following functions : 

(a) When the current is turned on, it must bring the carbons 
into contact. 

(b) It must then "strike" the arc by separating the carbons the 
proper distance. 

(c) As the carbons consume away, it must feed them together. 

(d) If the carbons approach too close, it must separate them. 

(e) If the arc goes out it must restrike it. 

(f) In a series arrangement, if the carbon burns out or breaks, 
a cut-out switch must operate to shunt the current by the dis- 
abled lamp. 



408 



ELEMENTS OF ELECTRICITY. 



When it is realized that the mechanical and electrical arrange- 
ments by which the foregoing objects are attained must differ 
according as the lamps are connected in series or in parallel, and 
also must differ according as direct or alternating current is to be 
used, it will be seen that the kinds of lamps are very numerous. 
We can do no more, therefore, than outline the principle of opera- 
tion of a few typical forms. 




518. The Clutch. — In all ordinary direct current arc lamps, the 
positive carbon is the upper one. There are two reasons for this. 
The first and principal is because eighty-five per cent of the light 
produced by the arc is emitted from the crater at the tip of the 
positive carbon and therefore this must be above so as to throw 
its illumination downwards. The second is because the positive 
carbon is consumed more than twice as rapidly as the negative, or 
in open arcs at the rate of about one and a half inches per hour 
and by placing it above it is in the best position to be fed by grav- 
ity. These considerations do not apply to alternating current 
lamps, nor to certain projectors and search lights. In this last 
rv\ class it is desirable that the crater should face 

the reflector and lie in its focus; the carbons are 
accordingly often placed horizontally, or one 
horizontal and the other vertical, and both may 
be fed automatically or by hand. The arrange- 
ment by which the upper carbon is lifted and 
held at the proper distance from the lower 
and by which it is allowed to slide down as 
it burns away, is called the clutch. There are 
many forms of clutches. Some operate like the 
tongs used in hoisting stones and close when 
they are raised but open when they are lowered. 
A very simple form is shown in section in Fig. 
248. This consists of a metal plate A pierced 
with a circular hole slightly larger in diameter 
than the carbon holder which passes through it. 
One end of this plate fits loosely in the jaws B 
of the lifting apparatus. As B rises, the plate A is canted and 
thus grasps the rod. When B is lowered, A strikes the stop C 
and is brought to a horizontal position, thus releasing the carbon 
which slips down. 



H 



CZ3 
C 



□O 



M 



Fig 



248 



ELECTRO-MAGNETICS. 



409 



519. Constant Potential Arc Lamp. — As stated above, arc lamps 
may be run in series or in parallel. The series arrangement is by 
far the more common, but the parallel grouping is also frequently 
employed, especialty for interior 
illumination. In this case the 
lamps are connected across mains 
between which a constant differ- 
ence of potential is maintained. 
One of these lamps is shown dia- 
grammatically in Fig. 249. With 
the carbons in contact, when the 
switch S is closed the current 
enters at A, passes through the 
resistance R, thence through the 
solenoid C to the upper carbon, 
down this to the lower carbon and 
out by B. The current passing 
through C causes it to suck up the 
plunger and, through the clutch, 
to raise the upper carbon and thus 
strike the arc. As the carbons 
burn away, the arc gets longer 
and its resistance increases. This 
reduces the current, and the lift- 
ing power of C grows less until finally it can no longer support 
the plunger and the carbon and they fall. The clutch strikes the 
stop and releases the carbon which slides down, shortening the 
arc. This increases the current and the plunger is again drawn 
up, and so on. 

Without the resistance R, the result of closing the switch with 
the carbons in contact would be in the nature of a short circuit 
(Par. 306). This resistance steadies the current by preventing 
violent fluctuations and it is therefore a "ballast' ' as described in 
Par. 508. 

520. Constant Current Arc Lamp. — For operating arc lamps 
in series, the generator and its regulator are designed so as to 
furnish a constant current, therefore, whether the arc be long 
or short the current is the same. On this account, resistance in 
series with the lamp is not required. Furthermore, the arrange- 
ment described in the preceding paragraph could not be used, for 




410 



ELEMENTS OF ELECTRICITY 



the pull of the solenoid upon its plunger being constant, the 
carbon would not feed. For such lamps the so-called "differen- 
tial" mechanism is employed. This is 
shown diagrammatically in Fig. 250. 
With the carbons in contact, the open- 
ing of the switch S causes the current 
entering at A to pass around the sole- 
noid to the point C, thence to the upper 
carbon, thence to the lower and out by 
B. The passage of this current actuates 
the clutch and strikes the arc. To 
cause the carbon to feed, a differential 
coil is taken off at the point C and con- 
nected at D, that is, it is in shunt with 
the arc. This coil is of many turns of 
fine wire and is wrapped in opposite 
direction to, and inside of the first, but 
for clearness is represented in the dia- 
gram as being below. The two coils 
being wrapped in opposite directions, 
the pull upon the solenoid plunger is 
lg " * due to the difference of the ampere 

turns in the two. With the carbons in contact, the difference of 
potential between E and D is very little, therefore, a very 
small current flows through the differential coil. As the car- 
bons draw farther and farther apart, the resistance, and 
consequently the difference of potential, between E and D in- 
creases. This causes an increasing current to flow through the 
differential coil and weakens more and more the pull on the 
plunger. A point is finally reached when the plunger drops and 
the carbon feeds. 

521. The Enclosed Arc. — The wasting away of the carbons in 
the ordinary arc lamp is mainly due to the combination of the 
white hot carbon vapor with the oxygen of the air. It is not 
practicable to enclose the carbons in air-tight globes but in recent 
years there has been introduced a form of arc lamp in which the 
arc is surrounded by a globe so fitted that the admission of air is 
reduced to a minimum, and in these the life of the carbons is very 
greatly prolonged, the consumption being reduced from 1.5 inches 
per hour to less than one-tenth of an inch. In addition to the sav- 




ELECTRO-MAGNETICS. 41 1 

ing in carbons, there is a very great saving in labor since the lamps, 
instead of having to be "trimmed" or supplied with fresh carbons 
daily, average over 100 hours and may be run as long as 200 hours 
without attention. Other advantages are a steadier light and 
absence of the hissing noise of the open arcs. The principal chan- 
nel for the admission of air to the arc is the space around the carbon 
since this latter must be free to be moved by the lamp mechanism. 
To reduce this, the carbons must fit the opening very accurately, 
for which reason, as already mentioned (Par. 516), pressed car- 
bons are used instead of the molded. 

522. The Flaming Arc. — With the common arc light, the carbons 
are from one-sixteenth to less than a quarter of an inch apart and 
the greater part of the light is emitted from the incandescent car- 
bons, although the maximum heat is developed within the arc 
itself (Par. 485). If it were possible to suspend within this arc 
a non-combustible solid, like the mantle of the Welsbach burner, 
it would be heated to incandescence and the heat energy of 
the arc would be converted into light energy. This object is 
partially realized in the so-called flaming arcs. In these, the 
positive carbon is either impregnated with certain salts of cal- 
cium or of magnesium or has a core filled with these salts. The 
vapor produced when these salts are volatilized is highly heated 
and emits a powerful reddish yellow light, and since it con- 
ducts it also permits the carbons to be separated by upwards 
of an inch. They need not be raised to such a high temperature 
as in the common arc lamps and therefore their life is longer. 
The efficiency of these lamps is at least three times that of the 
common form. 

Instead of the carbons being in the same vertical line, they are 
sometimes arranged both pointing downward like the letter V, 
the arc being at the vertex. In this way, neither carbon screens 
the other and both tips throw their light down. There is a tend- 
ency, however, for the arc to ascend between the carbons. This 
is corrected by arranging a magnetic field, similar to the magnetic 
blow-out (Par. 485), but only strong enough to keep the arc down 
at the tips of the carbons. 

An additional advantage of this arrangement is that the slag 
formed by the fusion of the impregnating salts drops off and does 
not clog the tips of the carbons with a non-conducting glassy 
material. 



412 ELEMENTS, OF ELECTRICITY. 

523. The Magnetite Arc Lamp. — The magnetite arc lamp, but 
recently developed and used with direct current only, resembles 
the flaming arc lamp in that the chief source of light is the arc 
which is an inch or more in length. It differs from other arc lamps 
in that little or no light is given off by the electrodes, also that the 
maximum amount of light is developed at the negative end of the 
arc. The positive electrode is of copper and is of such size that 
the heat developed is conducted away so that the electrode is not 
consumed. The negative electrode is a thin steel tube, the size 
and shape of an ordinary carbon. It is packed with a mixture of 
powdered magnetite, Fe 3 4 , and oxides of chromium and titanium. 
The magnetic oxide renders the electrode a conductor, the remain- 
ing oxides not conducting until they have been heated. The oxide 
of titanium imparts the luminosity to the arc; the oxide of chro- 
mium increases the life of the electrode. An eight-inch electrode 
in such a lamp with a current of 4 amperes at a pressure of 80 volts 
will burn for upwards of 200 hours. Since the constituents of the 
electrode are oxides, there is no combustion and the arc is not 
enclosed. These oxides, however, are volatilized and condense 
immediately beyond the limits of the arc in a reddish soot which 
if not removed soon covers globes, reflectors, etc. It is therefore 
necessary in these lamps to provide some form of chimney with a 
strong draught by which this deposit is carried off. 

524. Efficiency of Arc Lights. — The efficiency of an arc light is 
much greater than that of an incandescent lamp. The common 
arc lamp, carrying a current of about 10 amperes at a pressure of 
about 50 volts, develops 2000 candle-power in the zone of maxi- 
mum luminosity, or, in round numbers, one candle-power per 0.25 
watt. The mean spherical candle-power (Par. 509) is, however, 
considerably less than 2000. The larger search lights, taking 200 
amperes at 60 volts, develop nearly eight candle-power per watt, 
but it must be noted that there is a lack of agreement and much 
uncertainty as to the measurement of the candle-power of these 
powerful lights. 

525. Luminous Vapor Lamps. — Suppose a high voltage, such as 
that produced by an induction coil, be applied to two platinum 
wires sealed into the opposite ends of a glass tube, and suppose 
that at the same time an air pump be set to work to exhaust the 
air from the tube. If the wires be not too far apart, sparks will 



ELECTRO-MAGNETICS. 413 

pass between them, but as the air is exhausted, these sparks lose 
their definiteness and finally take the form of an effulgence or glow 
completely filling the tube. The color of this glow varies with the 
nature of the gas enclosed in the tube. For air, it is rosy pink; for 
nitrogen, yellow; for carbon dioxide, white. At this stage the rare- 
fied gas has great conductivity. If the exhaustion of the tube be 
continued, the conductivity decreases, the luminous column begins 
to break up in striae and finally disappears. When the pressure 
has been reduced to about one-millionth of an atmosphere, the 
glass itself begins to phosphoresce. Beyond this, the resistance 
becomes so great that no current can be sent through the tube. 
There is therefore a stage of rarefaction in which gases conduct 
electricity and in doing so emit light, and these effects diminish 
if the pressure be increased or decreased from what it is at this 
stage. Explanation of this will be given later; for the time being 
it will suffice to say that when highly rarefied these gases ionize 
and therefore conduct (Par. 276). If the exhaustion be complete, 
there are no ions left and consequently a vacuum is a non-con- 
ductor. 

The foregoing is the principle of the luminous vapor lamps, two 
of which we shall now describe. Their luminous efficiency is very 
high, for while in the ordinary carbon filament lamp less than one 
per cent of the total energy expended is developed as light, in 
these luminous vapor lamps twenty per cent or more is so develop- 
ed. They have not yet been made in small units but are rather 
used for general illumination of large spaces. 




mm 



Fig. 251, 



526. The Moore Light. — The apparatus for producing this 
light, shown diagrammatically in Fig. 251, takes the form of an 
exhausted glass tube one and three-quarters inches in diameter and 
of any length up to 200 feet. It is usually suspended along the 



414 ELEMENTS OF ELECTRICITY. 

ceiling of the room to be illuminated. When in operation, it emits 
a soft, diffused light, without flickering or unsteadiness, the color 
varying, as stated in the preceding paragraph, according to the 
gas contained in the tube. To produce a light of fifteen candle- 
power per running foot, about 70 volts per foot are required, the 
corresponding current being about one-third of an ampere. By- 
increasing the voltage, the candle-power can be raised to a maxi- 
mum of thirty per foot. A tube 100 feet long requires 7150 volts. 
This high voltage is obtained from an alternating current by means 
of a simple step up transformer, as shown in the figure above. 

As the lamp is used, the gas in the tube appears to be consumed 
and the rarefaction increases. This causes the resistance to in- 
crease. It therefore becomes necessary to introduce from time to 
time minute amounts of gas, and a simple and effective automatic 
valve has been devised for this purpose. 

527. The Cooper Hewitt Mercury Vapor Lamp. — If in a glass 
tube, otherwise vacuous, there be introduced a small amount of 
mercury, and if a part of this mercury be highly heated, as for 
instance by the production of a spark or an arc, it will throw off 
electrons into the vacuous space which will thereby be rendered 
conductive. A current passed through this vapor causes it to 
glow with a soft greenish light. 

Various forms of this lamp have been devised, all alike in princi- 
ple but differing in the arrangements for starting. A common 
form is shown in Fig. 252. This particular lamp, designed for use 
in a 100 volt circuit, and taking a current of three and a half 
amperes, consists of a one-inch glass tube, AB, 45 inches long and 
shaped as shown. It is supported by a frame CD, which carries 
the lead wires and which hangs from the suspension bar E. The 
canopy F contains the various coils and electro-magnets used in 
connection with the lamp. The tube is exhausted to a pressure of 
one millimeter. The positive electrode A is of iron, a metal to 
which mercury does not adhere, and the negative electrode B is a 
small puddle of mercury. 

To start the lamp, the ring attached to A is pulled down, the 
lamp and frame rotating about the point E until A is slightly 
below the level of B. The mercury in B flows down the tube 
and makes contact at A. This little stream of mercury between 
A and B would act as a short circuit were it not for a ballasting 
coil (Par. 508) in the canopy F. The ring is now released, the 



ELECTRO-MAGNETICS. 



415 



lamp tips back to its original position and the mercury runs back 
into B. In doing so, the thread of mercury breaks at some point 
producing a flash-like arc, volatilizing some of the metal and 
ionizing the vapor so that the lamp starts. This voltage at break 
is aided by an inductance coil in series. In the smaller sizes of 
lamps, this tipping is done by electro-magnets. Several other 
starting devices are in use. 




Fig. 252. 



The electrons, carrying negative charges, move from B to the 
positive electrode A, and this electron flow continues so long as 
the supply is replenished by the hot arc which plays about on the 
surface of B. Should this arc drop too far, either because of 
diminished voltage between A and B or because cf reversal of 
direction of current, the emission of electrons and the flow of 
current ceases. The effect* is as if a large resistance were suddenly 
introduced at the surface of the negative electrode. In order to 
start the current, the arc must be produced anew. 

This form of lamp can be used with direct current only, but 
others are made for use with alternating currents. The principle 
of these latter will be explained when the subject of the mercury 
arc rectifier is reached. 

, The efficiency of the light is high, being 0.64 watt per candle- 
power. It is rich in actinic rays and especially valuable for photog- 
raphy, blue printing, etc., but has one very grave objection. It 
is devoid of red rays and red objects placed in it appear purple or 
black. It imparts to persons a peculiarly ghastly appearance and 
can not be used where colors are to be shown in their proper rela- 
tion. No way has yet been discovered of adding the needed red. 



416 



ELEMENTS OF ELECTRICITY. 



CHAPTER 38. 

THERMO-ELECTRICS. 

528. Seebeck's Discoveries. — In 1821, in investigating Volta's 
contact series (Par. 187), Seebeck discovered that in a circuit com- 
posed of two metals, if one of the junctions be at a different tem- 
perature from the other, an E. M. F. and current will be produced. 
Fig. 253 represents a circuit composed of a strip of copper and one 




Fig. 253. 



of iron which are joined at the points A and B. The strips may be 
welded, or soldered, or simply pressed together. If the junction 
A be heated so that its temperature is higher than that of B, a 
current will flow around the circuit in the direction indicated by 
the arrows, that is, at the cool junction it will flow from the iron 
to the copper, and at the hot junction, from the copper to the iron. 
The needle placed within the circuit will indicate this current. 
The two metals constitute a thermo-couple, and the E. M. F. pro- 
duced is called the thermo-electric electro-motive force. Seebeck 
found further that this E. M. F. varied (a) with the metals used 
and (b) with the difference of temperature of the junctions, and he 
was able to arrange the following thermo-electric series in which, in 
a thermo-couple composed of any two, the current at the cold 
junction flows from the metal higher on the list to the metal which 
is lower. 



ELECTRO-MAGNETICS. 



417 



Thermo- Electric Series. 



Antimony 


Tin 


Iron 


Lead 


Zinc 


Copper 


Silver 


Platinum 


Gold 


Bismuth 



In accordance with these observations, thermo-couples are 
usually made of antimony and bismuth, though certain metallic 
sulphides may also be used. The E. M. F. produced is very feeble. 
Even for an antimony-bismuth couple, it is only about one ten- 
thousandth of a volt per degree Centigrade, or if one junction of 
such a couple be placed in boiling water, the other in melting ice, 
the E. M. F. will be about one-hundredth of a volt. 

529. Thermo -Electric Inversion. — In 1823 Cumming added to 
the discoveries of Seebeck by showing that the thermo-electric 




E. M. F. varied not only with the difference of temperature of the 
two junctions but also with their actual temperatures. Thus, if 
one junction of the copper-iron couple shown in Fig. 253 be kept 
at a constant temperature and the other be heated so that its tem- 
perature increases at a uniform rate, the E. M. F. will at first also 
increase uniformly but finally will slacken and will reach a maxi- 
mum at 275° C, after which it will decrease. This is shown 
graphically by the curve in Fig. 254, in which the abscissae repre- 
sent temperatures and the ordinates the corresponding E. M. F. 
The temperature Ot, at which the E. M. F. te is a maximum, is 
called the neutral temperature and varies for each different pair of 



418 ELEMENTS OF ELECTRICITY, 

metals. If the temperature of the junctions be equally distant 
from t, the E. M. F. is zero. Thus at 0T = 2x0t, the E. M. F. is 
zero and beyond T it is negative, hence the current is reversed and 
Or is called the temperature of inversion. Had the constant 
temperature of one junction been Of instead of 0, the maximum 
E. M. F. would have been me, the neutral temperature remaining 
unchanged. This thermo-electric curve has been shown by Lord 
Kelvin to be a parabola. 

530. The Peltier Effect. — From what has just been seen, if one 
junction of an antimony-bismuth thermo-couple be heated, as 



ANTIMONY a BISMUTH 



Fig. 255. 

shown in Fig. 255, a current will flow around the circuit as indi- 
cated by the arrows, that is, flowing at the cold junction B from 
the antimony to the bismuth. 

If the source of heat be now removed, the current will still con- 
tinue to flow so long as the junction A is at a higher temperature 
than the junction B. The only conceivable source of this current 
is the heat energy at A, and since this heat energy is converted 
into electrical energy, there must be at that point an absorption 
and disappearance of heat. Also, since the actual current through 
the junction B is opposite in direction to the current which would 
have been produced by the absorption of heat at that point, 
the logical inference is that heat is developed at B. The correct- 
ness of this inference was shown by Peltier in 1834. A bar of anti- 
mony and one of bismuth were placed crosswise as shown in Fig. 
256 and were soldered together. Between the ends C and B were 
connected a galvanometer G and a key S. Between A and D were 
connected a battery and a key K. K was closed for a while, 
allowing a current to flow around the triangular circuit in the 
direction DEA, or passing at the junction from the bismuth to 



ELECTRO-MAGNETICS. 419 

the antimony. K was then opened and S was closed. The gal- 
vanometer immediately indicated a current from C to B, showing 
that the junction E had been cooled below the temperature of B 
and C by the passage of the current from the battery. The battery 
was now reversed so that when K was closed the current flowed in 
the direction AED, or from the antimony to the bismuth. After 
a while, K was again opened and S closed. The galvanometer now 
indicated a current from B to C, showing that the junction E had 
been heated above the temperature of B and C. 




Fig. 256. 

We thus see that when a current is passed across the junction 
of two dissimilar metals, heat is evolved if the current flows from 
the metal that is the higher in the thermo-electric series (Par. 528), 
and heat is absorbed if it flows from the metal that is the lower 
in this series. 

This heating or cooling produced by the passage of a current 
across the junction of two dissimilar metals is called the Peltier 
effect, and is entirely distinct from the Joule effect discussed in 
Chapter 35. The Joule effect varies as the square of the current 
and is independent of the direction of flow; the Peltier effect varies 
as the first power of the current and is reversed if the direction of 
the flow be reversed. 

In the manufacture of very delicate electrical measuring instru- 
ments, consideration must be given to these various thermo-elec- 
tric effects. If in the circuit of such instruments a junction of 
different metals occurs, the heating effect of the current may set 
up thermo-electric effects which might cause appreciable error in 
the indications of the instrument. 



420 



ELEMENTS OF ELECTRICITY. 



531. The Thomson Effect.— Sir William Thomson (Lord 
Kelvin) showed that when a current flows through a homogeneous 
conductor which is heated at one point more than at another, heat 
is either developed or absorbed, depending upon the nature of the 
conductor and the direction of the current. Thus, in a copper wire 
whose center is hotter than the ends, heat is absorbed by the cur- 
rent as it flows towards the hot center and evolved as it flows from 
this center. With an iron wire, these effects are reversed, heat 
being developed in the first half and absorbed in the second. This 
Thomson effect has not been observed in lead and consequently lead 
is taken as the standard, or is made one of the elements in each 
thermo-couple which is tested in order to determine the thermo- 
electric power of the various metals. 

The subject of thermo-electricity is susceptible of elaborate 
mathematical treatment but its importance is not now sufficient 
to warrant a more extended discussion. We shall therefore pass 
at once to a description of some of its practical applications. 

532. The Thermopile. — Although, as stated above (Par. 528), 
the E. M. F. of a thermo-couple is very feeble, if a number of these 
couples arranged in the same order be connected in series and the 
alternate junctions be heated, the E. M. F.s will all act in the same 
direction and the total E. M. F. will be the sum of the separate 
E. M. F.s, in other words, the arrangement is similar to a battery 

composed of a number of cells con- 
nected in series. Such an arrange- 
ment is called a thermopile. 

Many forms of thermopiles have 
been devised. For example, the 
couples may be grouped as shown 
in Fig. 257 like the spokes of a 
wheel radiating from a central cy- 
lindrical opening, and there may 
be a number of these groups 
placed one above the other and all 
connected in series. The interior 
cylinder may then be heated by a 
small furnace, by gas jets, or by 

hot water, the outer ends of the couples being cooled by the air. 
At first sight it seems that the thermopile affords a satisfactory 

solution of an extremely important problem, the direct conversion 




Fig. 257. 



ELECTRO-MAGNETICS. 



421 



of heat energy into electrical energy without the usual interme- 
diate steps of heating water, producing steam, utilizing the expan- 
sion of the steam to produce rotation, and by means of this rota- 
tion producing electricity as outlined in Par. 423, each of which 
steps is accompanied by inevitable loss of energy. Thermopiles 
have been constructed to furnish the small currents required in 
gold and silver plating, and are used in certain extremely sensitive 
heat-measuring instruments (Par. 533), but where electricity is to 
be supplied on a large scale, they are a failure. The Joule effect, 
the Peltier effect and the heat conductivity of the two metals all 
tend to raise the temperature of the cool junctions and thus 
decrease the E. M. F., and the couples themselves deteriorate 
rapidly with use. Their efficiency is very low, less than one-half 
of one per cent of the heat energy being converted into electrical 
energy. 

533. The Radiometer. — There has been employed for the com- 
parison of radiant heat from different sources, a thermopile con- 
sisting of a rectangular bundle of thermo-couples arranged in series 
and mounted in a frame as shown in Fig. 258. The contiguous 




Fig. 258. 

couples and the metal strips of each couple, except at the junctions, 
are insulated from each other by sheets of mica. The first and 
last strips of the series are connected to terminals T, which are 
attached one on each side of the frame. The pile, except the end 
which is to receive the radiant heat, is shielded by a protecting 
hood. The receiving end is coated with lampblack, the best 
absorbent of heat. When in use, a sensitive galvanometer is con- 
nected to the terminals, the current through the galvanometer 
varying directly as the difference of temperature of the hot and 
cold faces of the pile. 



422 



ELEMENTS OF ELECTRICITY. 



Thermometers and pyrometers have been constructed on the 
principle of the thermopile. In the pyrometers, the couple is com- 
posed of platinum and rhodium. 

534. The Radio -Micrometer .—An extremely sensitive form of 
radiometer, the radio-micrometer , has been devised by Vernon 
Boys. It combines the principles of the thermo-couple and the 
d'Arsonval galvanometer. As shown diagram- 
matically in Fig. 259 it differs from the d'Arsonval 
galvanometer (Par. 378) only in that a quartz 
fibre is substituted for the phosphor-bronze sus- 
pension, and the coil consists of a single vertically- 
elongated loop of copper wire. To the lower ends 
of this loop there are soldered two small bars of 
antimony and bismuth and these bars are con- 
nected by a little sheet of lampblack-coated copper 
foil, only one-tenth of an inch square. When 
the copper foil is heated, the E. M. F. of the 
couple is very small but, since the resistance of 
the copper loop is also small, the current is ap- 
s ' ° ' preciable and the loop moves in accordance with 
Maxwell's law (Par. 371), the deflection being observed by means 
of the mirror M. It is said that a change in the temperature of 
the copper foil of one-millionth of a degree will cause a deflection 
of one division on the scale, and that the radiant heat of a candle 
can be detected at a distance of two miles. Instruments of this 
kind, known also as bolometers, have been used to measure the 
heat radiated from the stars and to compare the heat emitted 
from different portions of the solar spectrum. 




ELECTRO-MAGNETICS. 423 



CHAPTER 39. 

REMARKS ON CERTAIN ELECTRIC UNITS. 

535. Two Systems of Electric Units. — There are two distinct 
systems of electric units; one, the electro-static, based upon the 
interaction of static charges; the other, the electro-magnetic, based 
upon the interaction of a magnetic pole and the field produced 
about a conductor carrying a current. The electro-magnetic units, 
and the derived practical units, are, on account of their suitability 
for practical purposes, used to the exclusion of those of the electro- 
static system. Nevertheless, it is desirable for the student to be 
acquainted with both systems and to understand the relation ex- 
isting between them. 

In the electro-static system, the starting point is the unit quan- 
tity, which is denned (Par. 56) as that quantity which when placed 
at a distance of one centimeter in air from a similar and equal 
quantity, repels it with a force of one dyne. 

In the electro-magnetic system, the starting point is the unit 
pole, or (Par. 133) that pole which, when placed at a distance of one 
centimeter from a similar and equal pole, repels it with a force of 
one dyne. 

536. Units of Current and Quantity. — Thus far, there does not 
seem to be much to choose between the two systems. In the next 
step, however, there is a marked difference. 

In the electro-static system the unit current is that current 
which conveys unit quantity in unit time. 

In the electro-magnetic system, the unit current can not be 
defined so simply. We have shown, however (Par. 353), that a 
current flowing in a conductor establishes about that conductor 
a magnetic field which varies directly with the current. There- 
fore, with other conditions constant, we may take the strength of 
the field produced as a measure of the strength of the current, and 
the simplest way to compare magnetic fields is to compare the 
forces which they exert upon the same pole. -The electro-magnetic 
unit of current is therefore defined (Par. 355) as that current which, 



424 ELEMENTS OF ELECTRICITY. 

flowing through one centimeter of a conductor bent into the arc of 
a circle whose radius is one centimeter, exerts a force of one dyne 
upon a unit pole placed at the center of the circle. This current, 
we have seen, is ten amperes. 

Having thus defined the unit current, we may now define the 
electro-magnetic unit of quantity as that quantity conveyed by 
unit current in unit time. The ampere flowing for one second 
conveys one coulomb; the absolute unit of quantity is therefore 
equal to ten coulombs. It is thus seen that in the electro-static 
system we pass from unit quantity to unit current; on the other 
hand, in the electro-magnetic system, we pass from unit current 
to unit quantity. 

By experiments and measurements based on widely different 
methods, it has been found that the electro-magnetic unit of 
quantity is about (2.98 + )(10 10 ) times as great as the electro- 
static unit of quantity. For round numbers, this is taken as 
3xl0 10 , or thirty billion. The coulomb, therefore, as has already 
been stated (Par. 56), is three billion (3xl0 9 ) times as great as 
the electro-static unit. 

537. Units of Electro -Motive Force. — In either system, unit 
difference of potential exists between two points when the expendi- 
ture of one erg is required to convey a unit of quantity of elec- 
tricity from one to the other. The electro-magnetic unit of poten- 
tial is therefore ~ ^nib times the electro-static unit of potential. 

o X 1U 

In Par. 427 it was stated that 10 8 absolute electro-magnetic units 
of potential were equal to one volt. The volt is therefore 3 X 10 10-8 
= 3 X 10 2 = 300 times as small as the electro-static unit of potential, 
or, as was stated in Pars. 77 and 78, the electro-static difference of 
potential in ergs must be multiplied by 300 to reduce it to volts. 

538. Primary Electro-Magnetic Units.— The units of E. M. F., 
current and resistance are bound together by Ohm's law, / = E/R, 
which necessarily is true whatever units be employed, that is, 
whether we use the absolute or the practical units. It follows that 

absolute unit of E. M. F. 



absolute unit of current 



absolute unit of resistance 



If, therefore, any two'of these units be fixed upon, the third follows 
as a matter of course; or, it suffices to define any two, and these 



ELECTRO-MAGNET ICti. 425 

definitions fix the third. It was this consideration that led to the 
definition of resistance as a ratio, to which definition attention was 
called in Par. 307. 

The question now arises, which two shall be selected as our 
primary units. 

In Par. 355, the definition of the absolute unit of current was 
given (repeated in the preceding paragraph), and in Par. 374 it was 
shown how by means of the tangent galvanometer a current could 
be measured in absolute units. The absolute unit of current is 
therefore selected as one of the primary units. 

Reflection will show that of the three units, resistance is the only 
one which could be perpetuated in a material standard, such as a 
given length of a certain-sized wire of a specified material. If 
resistance could be measured absolutely, it would naturally be 
selected as the second primary unit. We shall now explain how 
this may be done, but preliminary thereto we must develop an- 
other conception of electric resistance. 

539. Dimensional Formulae. — It has been shown (Par. 10) that 
the fundamental units of our system are the centimeter, the gram 
and the second, and that all the other units are derived from these. 
It is therefore possible to express any derived unit in terms of 
length, mass and time. Such expressions are called the dimensional 
formulae of the units in question. A study^ of these dimensional 
formulae will afford a clearer conception of the nature of the units 
and will bring to light unexpected relations. 

540. Dimensional Formulae of Electro-Magnetic Resistance. — 

From Ohm's law, R = E/I. E, the difference of potential, is meas- 
ured by the work done in moving unit quantity of electricity 
through a difference of potential E. If to move Q units the work 
done is W, then to move one unit, the work is W /Q, whence 

W 

But work = force X path =FxL, and Q = IxT. Substituting 
these values in (I) F X L 

Substituting this for E in Ohm's law 

R = ~Xji (II) 



426 



ELEMENTS OF ELECTRICITY. 



Two poles, each of strength m, at a distance L apart exert upon 
each other a force F = m 2 /L 2 , whence 

m = VFJ? (Ill) 

A pole of strength m placed in a magnetic field of strength H is 
acted upon by a force F = m.H, whence H = F/m. 

The field produced at the center of a circular coil by a current 
/ (Par. 354) is proportional to I/L, or H = I/L t L being the radius 
of the coil. Equating these two values of H and solving for m, we 
have m = F.L/I. 

Substituting this value of m in (III), and solving, we have 
F = I 2 , whence (II) becomes 

R = L/T 

But L is length and T is time, hence resistance is of the nature 
of a velocity. 

541. Resistance Expressed as Velocity. — Why it is possible to 
express resistance as a velocity may be shown as follows: Let Fig. 

AMMETER 





1^^ 



Fig. 260. 

260 represent the arrangement of parallel rails and sliding cross 
bar which we have already described several times. Suppose the 
rails to be of negligible resistance, to be one centimeter apart and 
to embrace between them a uniform unit field. AB, moving with 
uniform velocity, is slid along towards D, which is at an indefinite 
distance to the left. If A B moves V centimeters per second it will 
cut V lines of force and will generate V absolute units of E. M. F., 
in direction from A to B (Par. 422). If the resistance of AB be R, 
the current through AB will be 

'-i 

Since the current varies directly with V, the velocity of AB, it 
is possible to move AB rapidly enough to make I one absolute 
unit of current. When / becomes 1, the above expression becomes 
R = V, or R is expressed as a velocity. 



ELECTRO-MAGNETICS. 427 

If R be one ohm, in order to drive a current of one absolute unit 
through AB, it must be moved with a velocity of 10 9 centimeters 
(ten million meters, or one earth's quadrant per second (Par. 4) ). 

From the foregoing, knowing the strength of the field between 
the rails and the velocity with which AB is moved, we could deter- 
mine V. The current in the circuit could be read from an ammeter 
at D. Thus having V and I, the quotient of the former by the 
latter would give R, the resistance oi AB. Practically, such a 
determination is impossible. AB could not be moved for a suffi- 
cient length of time with the desired rapidity; it would not, as it 
moved, maintain unvarying contact with the rails; and finally, 
the resistance of the rails is not negligible, hence the resistance of 
the circuit would continually decrease. However, several methods 
have been devised by which these difficulties are obviated and we 
shall now explain one, first proposed by Weber and improved by 
later investigators. 

542. Absolute Measurement of Resistance. — In Fig. 261, AB 
represents a circular coil of a number of turns of wire, the ends of 




Fig. 261. 

the coil being joined together. It is mounted upon a vertical axis 
about which it may be spun rapidly. Through an opening in the 
top there extends a silk fibre from which there hangs at the center 
of the coil a needle. The arrows H represent lines of force of the 
earth's field. If the coil, viewed from above, be spun in a clock- 
wise direction, it will cut the lines H and consequently an E. M. F. 
will be induced. Application of the right hand rule (Par. 422) will 
show that as the side B moves from B to A, it will generate an 
E. M. F. acting upward and during the same time a downward 



428 ELEMENTS OF ELECTRICITY. 

E. M. F. will be generated in the side A, that is, there will be in- 
duced in the coil a current, which, viewed from the point P (a 
point on the horizontal axis of the coil perpendicular to the meri- 
dian), will be counter-clockwise in direction. As B passes the 
position A, and A passes the position B, the direction of the E. M. 

F. in B and in A, and consequently the direction of the current in 
the coil, is reversed, but at this same instant the opposite face of 
the coil is presented to P, so that viewed from P, the current 
flowing around the coil is always in the same direction. This cur- 
rent is pulsating. It is zero when the plane of the coil is at right 
angles to the magnetic meridian, and it is a maximum when this 
plane coincides with the meridian, hence it rises and falls with 
every half revolution of the coil. At the instant when the plane 
of the coil coincides with the magnetic meridian, the instrument 
is in principle the same as a tangent galvanometer (Par. 373), 
and at all times it may be regarded as a tangent galvanometer 
traversed by a current whose value is a mean of the instantane- 
ous values of the current. The suspended needle will be deflected 
accordingly. 

The induced E. M. F. will vary directly with the rate of cutting 
of the lines of force embraced by the coil. The number embraced 
is irr 2 H, r being the mean radius of the coil. The rate at which 
these are cut varies with a>, the angular velocity of the coil, and 
with n, the number of turns in the coil. If R be the resistance of 
the coil, the current through it is proportional to 

Tr.r 2 . H.n.co 
R 

The field produced at the center of the coil is (Par. 354) 

J ~ L x ir~ r 

If the needle be deflected through an angle 8, we have (Par. 146) 

p — - = H. tan 8 

whence 

r, 2ir 2 n 2 rco 

■K = ~z ;r 

tan 8 



ELECTRO-MAGNETICS. 429 

But rco is the actual velocity of a point at the extremity of the 
horizontal diameter of the coil. Calling this v, we have 

R = 7 -.v 

tan 8 

whence we see that the resist- 
ance of the coil is equal to the product of a velocity by a numerical 
factor. In the expression above, n and r are constants of the in- 
strument and a? and 8 are determined by observation. It will be 
noted that it is not necessary to know the strength of the needle or 
the intensity of the field H. If v be expressed in centimeters per 
second, R will be in absolute units of resistance. 

In actually carrying out the above determination, many 
delicate refinements were observed. These are described in detail 
in the Report of the British Association for the Advancement of 
Science for the year 1864. 

Resistance has been measured absolutely by several other 
methods. 

543. The Ohm. — As a result of the experiment outlined in the 
preceding paragraph, the investigators became possessed of a coil 
of wire whose resistance in absolute units was accurately known. 
The absolute unit being excessively small, the next step was to 
select a practical unit which should be based upon this absolute 
unit. It has been shown (Par. 284) that the need for a unit of 
resistance had been felt for some time. The resistance coils made 
by Ohm could not be standardized. In 1860 Siemens denned as 
a unit of resistance a column of pure mercury one meter long and 
one square millimeter in cross-section, the mercury being at a 
temperature of 0° C. Electricians had become accustomed to 
this unit and the German scientists especially were loath to give 
it up. The practical unit of resistance, the ohm, was accordingly 
chosen so as to agree as nearly as possible with Siemen's unit, and 
was denned as 10 9 absolute units of resistance, or (Par. 291) as 
the resistance of a column of mercury, one millimeter in cross- 
section and 106.3 centimeters in length, at a temperature of 0° C. 
It was later found more convenient to retain the length of the 
column but to specify the quantity of mercury in terms of weight, 
or as 14.4521 grams. 

544. The Ampere. — We have seen above (Par. 538) that the 
absolute unit of current had been determined from the tangent. 



430 ELEMENTS OF ELECTRICITY. 

galvanometer. It remains now to fix the practical unit of currento 
The existing practical standard of E. M. F. was that of the Daniell 
cell (Par. 206). This applied to the practical unit of resistance, 
the ohm, should drive through it the unit current. This current 
was found to be very nearly one-tenth of the absolute unit. The 
practical unit of current, the ampere, was therefore selected as 
exactly one-tenth of the absolute unit. Its definition has already 
been given (Par. 228). 

545. The Volt. — The selection of the primary practical units 
of resistance and current also fixed the volt, the practical unit of 
E. M. F. From Ohm's law, E = IR. Since / = 10" 1 absolute units 
of current and R = 10 9 absolute units of resistance, E = 10 -1 X 10 9 
= 10 8 . The volt was therefore defined as 10 8 absolute units of 
E. M. F. 

546. Resume. — The following resume will show the thread of 
connection between the successive steps in the adoption of the 
absolute and the practical electro-magnetic units. 

(a) The absolute unit of current was determined by means of 
the tangent galvanometer. 

(b) The absolute resistance of a coil of wire was determined by 
rotating the coil. 

(c) From this was determined the absolute unit of resistance. 

(d) This was found to be about .954 XlO -9 of Siemen's mercury 
unit, already in use. 

(e) To disturb this standard as little as possible, the practical 
unit of resistance, the ohm, was taken as 10 9 absolute units of 
resistance. 

(f) The existing practical standard of E. M. F. was that of the 
Daniell cell (1.07 volts) and it was desirable to disturb this as 
little as possible. 

(g) A Daniell cell applied to a circuit of one ohm drove through 
it a current which was very slightly greater than one-tenth of the 
absolute unit of current. 

(h) The practical unit of current, the ampere, was taken as 
exactly one-tenth of the absolute unit of current. 

(i) The selection of the practical units of resistance and current 
involved that of E. M. F., the volt, since the three units are 
bound together by Ohm's law. The volt is, therefore, 10 8 absolute 
units of E. M. F. 



ELECTRO-MAGNETICS. 43 1 

547. Comparison of the Dimensional Formulae in the Two 
Systems. — A comparison of the dimensional formulae of the units 
in the two systems will point to the contradictory conclusion that 
they do not agree. As an example, let us compare the dimensional 
formulae of the units of quantity. 

In the electro-static system, we have from Coulomb's laws for 
the force exerted between _two equal quantities Q (Par. 56), 
F = Q 2 /L 2 , whence Q = L VF. In mechanics it is shown that 
force = mass X acceleration, or F = MxL/T 2 . Substituting this 
value of F in the expression above, we have for the electro-static 
dimensional formula of quantity 

Q = LVWX/T (I) 

In the electro-magnetic system, Q = IxT = (E/R)xT. In 
Par. 540 it was shown that E = FxL/Q and that R = L/T, 
whence the electro-magnetic dimensional formula of quantity is 

Q = VmJ, (II) 

Comparing (I) and (II), we see at once that they are not the 
same, and that the ratio of (I) to (II) is L/T, a velocity. 

In a similar manner may be determined the dimensional 
formulae of the remaining units of current, capacity, potential 
resistance, and inductance as given in the following table : 

Unit Electro-static Electro-magnetic Ratio 

Current LVmX/T* VWL/T L/T = V 

Quantity LVM.L/T VM.L L/T = V 

Capacity L T 2 /L_ D/T 2 = V 2 

Potential VWX/T LVM.L/T* T/L = l/V 

Resistance T/L L/T T 2 /L 2 = l/V 2 

Inductance T 2 /L L T 2 /L 2 = l/V 2 

The V which enters all of these ratios has been determined in 
widely different ways by a number of observers and found to be 
3xl0 10 , or thirty billion, centimeters per second. This is the 
velocity of light. 

548. Explanation of Lack of Agreement. — It is on the face of 
it absurd that like quantities should have different dimensional 
formulae, and also that these formulae should contain such 
irrational quantities as the square root of a mass and of a length. 
Consideration will show that this state of affairs results from our 
failure to take into account in the formulae above the dielectric 



432 ELEMENTS OF ELECTRICITY. 

coefficient K (Par. 90) in the case of the electro-static units, and 
the permeability /* (Par. 392) in the case of the electro-magnetic 
units. The medium being air, these factors are both unity and 
hence are of no arithmetical effect, but in omitting them we are 
not justified in ignoring their dimensions. What these dimensions 
are, we do not know, but that' they account for the lack of agree- 
ment in the dimensional formulae of the two systems the following 
will show. 

In the preceding paragraph, in determining the dimensional 
formula of the electro-static unit of quantity, our assumed ex- 
pression for the force between two equal quantities Q should have 
been (Par. 90) F =Q 2 / K L 2 

whence Q = LVK^VmX/T (I) 

Likewise, in determining the dimensional formula of the electro- 
magnetic unit of quantity, the expression for the force between 
two equal magnetic poles should have been (Par. 133) 

F=m 2 /u.L 2 
whence 



m = LV}j,.VM.L/T 

The force exerted by a current I, flowing in a circular coil of 
radius L, upon a pole m at the center of the coil is proportional to 
ml/L (Par. 355), whence 

/ = F.L/m 

Substituting the value of m above and multiplying by T, we 
have, since Q = IxT 

Q = VM.L/V» (II) 

Equating the second members of (I) and (II) and solving 

L_ 1 
T y/Kii 

We see then that while the dimensions of the separate factors 
K and ji are unknown, the reciprocal of the square root of their 
product is a velocity, and therefore they can not be disregarded. 

This velocity, as stated in the preceding paragraph, is the 
velocity of light, and is also the velocity with which electric 
waves travel through space. As will be shown later it has an 
important bearing on Maxwell's electro-magnetic theory of light. 
(Par. 690.) 



ELECTRO-MECHANICS. 433 



PART V. 
ELECTRO-MECHANICS. 



CHAPTER 40. 

DIRECT CURRENT GENERATORS. 

549. Electro -Mechanics. — Electro-Mechanics, the subject which 
we are now to take up, is a more or less artificial division in- 
tended to embrace the production of electric currents by machin- 
ery, a consideration of these mechanically generated currents, and 
finally their employment to operate other machines. 

Electricity, no matter how produced, is always the same agent 
and the principles which have been developed in the preceding 
pages suffice to explain all the facts which we shall now bring out. 
The currents produced by machines are, however, more or less 
pulsating and are often alternating, that is, they periodically 
(usually many times a second), change their direction. These 
rapid changes in the current give rise to certain phenomena which 
renders it desirable to consider these currents in detail. 

550. Classes of Electrical Machines. — Electrical machines are 
primarily of two classes, generators and motors. The former, also 
called dynamos, transform mechanical energy into electrical energy 
and therefore deliver electrical energy to a circuit. On the other 
hand, motors transform electrical energy into mechanical energy 
and therefore receive electrical energy from a circuit. 

Machines are further classed according as they are designed to 
deal with direct currents or with alternating currents. We shall 
now consider generators of the former class. 

551. Coil Rotating in a Magnetic Field.— Suppose CD, Fig. 262, 
to be a coil in the magnetic field NS and free to rotate about the 
axis AB. Suppose its initial position to be, as shown in the figure, 
with its plane perpendicular to the lines of force of the field. It 



434 



ELEMENTS OF ELECTRICITY. 



now embraces the maximum number of these lines, and the first 
effect of rotation about A B, whether clockwise or counter-clock- 
wise, will be to decrease this number. This change will develop 
in the coil an induced E. M. F. whose direction may be determined 
by application of the rule given in Par. 421. It is simpler, however, 
to apply the right hand rule given in Par. 422, whence we see at 
once that whether the rotation be clockwise or counter-clockwise, 
as the side C of the coil rotates 180° from the position C to the 




Fig. 262. 



position D, there is an E. M. F. induced in C from rear to front, 
while as it rotates from D to C, the E. M. F. induced is from front 
to rear. The E. M. F. is reversed in direction whenever the coil 
passes through the perpendicular plane, and is zero when the 
coil lies in it, for which reason this plane is called the neutral 
plane. 

552. Calculation of E. M. F. of Rotating Coil.— The E. M. F. 

induced by the rotation of a coil in a magnetic field is from Par. 
426 equal to the rate of decrease of the number of lines of force 
embraced by the coil. If the field be uniform, this E. M. F. may 
be calculated as follows. Let ab, Fig. 263, be the primary position 
of the coil, its plane at right angles to the field. Its E. M. F. at 
any point, such as d, is measured by the rate of decrease at that 
point of the number of lines embraced. 

Let the total field embraced by ab be N. Let the coil make n 
revolutions per second, that is, let its angular velocity be 2irn. 
If ca, the radius of the circle described by a, be R, the actual 
velocity of a is 2irnR per second. At h the coil is moving at right 
angles across the field with a velocity which in one second would 



ELECTRO-MECHANICS. 



435 



carry it a distance hk. The total width of the field being 2R, it 

would be crossed in ~ — ^ = — seconds, and in this time N lines 

of force would be cut by each side of the coil, therefore, the E. M. F. 
being generated at h is 

2irnN 



E 



1/wn 



a 



JC2 



:g± 



^:d 



2S. 



^ 



^f 



n:e: 



$h: 



b 

Fig. 263. 

If the coil consists of S turns, the E. M. F. is 2irnNS. To con- 
vert this to volts, it must be divided by 10 8 (Par. 427), whence 
finally 

E=2mrNS/W volts. 

Should the coil at d continue to move for one second in the 
same direction and at the same rate as at d, it would move a dis- 
tance de=hk and in doing so would cut across the lines between 
/ and e. If the angle dca through which the coil has turned from 
its primary position be 0, then fe = de. sin 0. At the same time, 
the other side g of the coil is cutting across the field at this same 
rate, the total decrease being 2de. sin 6. Since de = hk, the E. M. F. 
being generated at d is 

2mrNS 



E 



10* 



•sin d 



Or placing C for the coefficient of sin d, 

E=C. sin d 

For the present it is sufficient to bear in mind that the E. M. F. 
generated by a coil rotating in a uniform field varies as the sine 
of the angle through which the coil has turned from its primary 
position at right angles to the field, that is, from the neutral plane. 



436 



ELEMENTS OF ELECTRICITY. 



553. Production of Current by Rotating Coil.— In Fig. 264 let 
CD represent a coil rotating about the axis XY in the magnetic 
field NS, and suppose that instead of being a closed coil, the end 
C terminates in a ring A, and the end D in a ring B, these rings 
being attached to the axis upon which the coil rotates, but being 
insulated from it and from each other. In Par. 551 it was shown 
that as the coil rotates 180° from its present position at right 




Fig. 264. 

angles to the field, an E. M. F. is generated from rear to front in C 
and from front to rear in D. No current is produced because the 
circuit is broken between the rings. If now a metal strip E be 
pressed against the ring A, and a second strip F be pressed against 
B, and these strips be connected by a wire, the circuit will be 
completed and a current will flow through the coil and wire as 
indicated by the arrows. A and B are collector rings, E and F are 
brushes, and the wire connecting these brushes is the external 
circuit. 

554. Alternating Current. — The resistance of the arrangement 
just described being constant, the current in the external circuit 
varies directly with the E. M. F. generated in the coil and this, 
we have seen (Par. 552), varies as the sine of the angle through 
which the coil has rotated from its position in the neutral plane. 



ELECTRO-MECHANICS. 



437 



Thus, at the instant shown in Fig. 264, the current in C is zero, 
but as C moves, a current flows towards A, reaching its maximum 
value when the coil has turned through 90° or has become parallel 
to the lines of force of the field. From this point, the current 
diminishes and is again zero when C has turned through 180° or 
has reached the position D. As C passes this point, the current 
again starts up, but it is now reversed, that is, it flows away from 
instead of towards A, and it consequently is also reversed in the 
external circuit. If the original direction be considered positive, 
this last must be considered negative. The current therefore 
reaches a negative maximum when C has turned through 270°, 
returns to zero when C reaches its primary position, and again 
reverses as C passes through this position. 

To an E. M. F. and current which thus pass through these 
periodic fluctuations and reversals, the term alternating is applied. 

555. Graphic Representation of Alternating E. M. F. and Cur- 
rent. — In Fig. 265 let B represent the cross-section of a coil rotat- 
ing about as a center and in a uniform field whose positive 




Fig. 265. 



direction, as indicated by the arrows, is downwards. AD is there- 
fore the neutral plane. Should the coil start at A, the direction 
of the induced E. M. F. is independent of the direction of rotation, 
that is, whether the coil rotates in a clockwise or in a counter- 
clockwise direction, the E. M. F. will act out from the plane of the 
paper. However, to conform to the trigonometric convention as 
to the direction in which angles are to be measured, we shall 
assume the rotation to be counter-clockwise. From Par. 552, the 
induced E. M. F. at any point B is proportional to BN, the sine 
of the angle 6 through which the coil has rotated. If, therefore, 
we lay off on a horizontal axis, AA, distances proportional to the 



438 ELEMENTS OF ELECTRICITY. 

angles through which the coil has turned, and at the points so 
determined erect ordinates upon which we lay off distances pro- 
portional to the sines of the corresponding angles, the sine or 
harmonic curve drawn through the extremities of these ordinates 
will represent the successive values of the E. M. F. For example, 
the point R is determined by laying off AM proportional to AB, 
and MR proportional (in this case equal) to NB. 

The curve shows what was stated in the preceding paragraph, 
that is, that the E. M. F. is zero at A, rises to a maximum when the 
coil reaches C, decreases to zero at D where it reverses, reaches a 
negative maximum at E and returns to zero at A, and so on. 

In the case under consideration, the E. M. F. acting towards 
the observer is considered positive, but this is purely a matter of 
convention and it is immaterial whether we regard it as positive 
or negative provided that the E. M. F. induced as the coil rotates 
from A to D be opposite in sign to that induced as it rotates from 
D to A. If the direction of the field be reversed, the direction of 
the E. M. F. is also reversed. 

Since the current varies directly with the E. M. F., we may take 
this same sine curve as representing the current also, or we may 
represent the current by another sine curve of the same periodicity 
but of different amplitude. From Ohm's law, I = E/R, we see 
that I and E are numerically equal only when R is unity. If R 
be less than unity, I is numerically greater than E and would be 
represented by the outer broken curve in Fig. 265. If R be greater 
than unity, / would be represented by the inner broken curve. 

Reflection will show that the abscissae of these sine curves may 
also be laid off on a scale of time, the distance A A corresponding 
to the time of one complete revolution of the coil. 

556. Rectification of Alternating Current. — Fig. 266 represents 
the same arrangement of a coil rotating in a magnetic field as 
described in Par. 553, only in this case the ends of the coil termi- 
nate in the copper semicircles or segments A and B instead of in 
two separate rings. These segments are likewise mounted upon 
the shaft of the coil, insulated from it and from each other. The 
brush E presses against the segment A; the brush F against the 
segment B. For simplicity of description, suppose the rotation 
to be clockwise. As C moves from its present position to the 
position D, the induced E. M. F. acts towards A, and current will 
therefore enter the external circuit by the brush E and leave it 



ELECTRO-MECHANICS. 



439 



by the brush F. As C, having reached the position D, passes 
through the neutral plane, the induced E. M. F. becomes zero 
and immediately thereafter reverses, that is, acts from A and 




Fig. 266. 

towards B. But also, as the coil passes through the neutral plane 
the brushes slip across the gap between the segments and E is 
now in contact with B, while F is in contact with A, therefore, 




Fig. 267. 

current still flows out into the external circuit through the brush 
E and the direction of the current in the external circuit remains 
unchanged. 



440 ELEMENTS OF ELECTRICITY. 

This is shown graphically in Fig. 267. The sine curve A repre- 
sents the alternating current (and E. M. F.) in the coil. B 
represents the current in the external circuit, the negative loops 
of the curve A having been reversed and made positive. 

An alternating current which has thus been made unidirectional 
is said to be rectified. The split ring, or arrangement of copper 
segments by which this is brought about, is a commutator, and the 
process is called commutation or rectification. We shall see later 
that an alternating current may be rectified otherwise than by a 
commutator. 

557. Increase in Number of Turns of Coil. — If the rotating 
coil, instead of consisting of a single turn, be composed of several 




Fig. 268. 

as shown in Fig. 268, an approximately equal E. M. F. will be 
induced in each. Examination of the figure will show that these 
turns being connected in series, the total E. M. F. is the sum of 
the separate E. M. F.s, or increases in proportion to the number 
of turns. The resultant E. M. F. of the coil is represented graph- 
ically by a sine curve of the same periodicity as the curves in Fig. 
267 but of an amplitude greater in proportion to the number of 
turns. 

Although the E. M. F. is thus increased by increasing the 
number of turns, practical considerations place a limit upon the 
number that may be added. Thus, the resistance of the coil 
increases directly with the number of turns and it is important 
that this resistance should be kept very small. The diameter of 
the wire, already large, must therefore be increased, and the wire 
is further enlarged by an insulating covering. In the actual 



ELECTRO-MECHANICS. 



441 



machines, the space in which these wires are wound is restricted, 
being usually a narrow groove or slot in the surface of a cylindrical 
body, and therefore the number of turns seldom exceeds six or 
eight. 

558. Increase in Number of Coils. — For a considerable portion 
of the time during the rotation of the single coil described in the 
preceding paragraphs, the induced E. M. F. is small, and twice 
during each complete revolution it is zero. If there be mounted 
upon the same axis a second coil whose plane is at right angles to 
that of the first (Fig. 269), the induced E. M. F. in this second 




Fig. 269. 

coil will be a maximum at the instant when it is zero in the first 
coil, and also it will be zero in the second coil when it is a maximum 
in the first. By a suitably arranged commutator we may always 
draw current from that coil whose E. M. F. is the greater, and 
thus avoid the periodic dropping to zero. For example, suppose 
the commutator to consist of four segments to which the coils are 
connected as indicated in the figure. At the instant represented, 
the E. M. F. in A A, the vertical coil, is zero, and that in BB, the 
horizontal coil, is a maximum, and it is this latter coil which is 
sending current out into the external circuit. As the coils rotate, 
the E. M. F. in BB decreases, that in A A increases, and these 
reach equality when the coils have turned through an angle of 45°. 
At that moment, the brushes are across the gap between the seg- 
ments and in contact with both. At the next instant, the brushes 
are in contact with the segments connected to the A A coil, in 
which coil the E. M. F. is rising to a maximum. These changes 



442 



ELEMENTS OF ELECTRICITY 



are shown graphically in Fig. 270. The broken and dotted curve 
represents the rectified E. M. F. in the BB coil; the broken curve 
represents the same in the A A coil. The maxima follow at inter- 
vals of 90° and midway between these maxima, as indicated by 
the intersection of the curves, the E. M. F.s are equal. The 
unbroken portion of these curves represents the E. M. F. (and 




current) in the external circuit. We therefore see that by inserting 
the second coil we obtain a current which, while pulsating, does 
not drop to zero as did the current from the original coil. If still 
other coils be inserted between these two, we may obtain a cur- 
rent which fluctuates less and less, and approaches constancy as 
the number of coils is increased. 

559. Open and Closed Coils. — Consideration of Fig. 269 will 
reveal the fact that except for the very brief instant when the 
brushes slide across the gap between the commutator segments, 
only one coil at a time supplies current to the external circuit. 
Thus, while the coil BB is supplying current, the coil AA is open 
at the commutator end and contributes nothing. The E. M. F. 
induced in these coils while the corresponding commutator seg- 
ments are not in contact with the brushes is represented by the 
broken portions of the curves in Fig. 270. This E. M. F. is not 
utilized. An arrangement in this manner of the coils of a generator 
is called an open-coil winding. 




We shall shortly see (Par. 569) that there is possible another 
arrangement by which the various coils may be connected in 
series and thus instead of being idle during a portion of the rotation 
they all constantly contribute to a resultant E. M. F. This ar- 



ELECTRO-MECHANICS. 443 

rangement is called a closed-coil winding. Points on the curve 
RR r , Fig. 271, representing this resultant E. M. F. are obtained 
by adding the corresponding ordinates of the component curves. 
It is seen that as the number of coils is increased, not only 
does the resultant E. M. F. increase but also the loops in the 
curve RR' become greater in number and smaller in amplitude, 
that is, the E. M. F. becomes less pulsating and more nearly 
constant. (See also Problem 399, Appendix.) 

560. Essential Parts of D. C. Generator. — The essential parts 
of a D. C. generator are — 

(a) A magnetic field. 

(b) Rotating coils. 

(c) A commutator. 

(d) Brushes. 

The coils and commutator and the shaft to which they are 
attached and with which they rotate are known collectively as 
the armature. The coils are usually inserted in grooves or slots 
in an enlarged portion of the shaft called the armature core. The 
portions of the coils on the exterior of the armature core and 
parallel to the axis of the shaft are called inductors. 

561. The Field. — The magnetic field in which the armature 
revolves is produced by field magnets, which may be either per- 
manent or electro-magnets. Permanent magnets can not be 
controlled nor can they be made of the size and strength required 
in large machines and they are therefore restricted to such small 
generators as those used to operate the call bell of a telephone or 
the sparking apparatus of a gasoline engine. In all important 
generators, electro-magnets are employed. It is to this class of 
generators that we refer in the following pages. 

Whatever be the external appearance of the generator, analysis 
will show that the field magnets are in principle horseshoe magnets, 
each consisting of a yoke and two limbs, the ends of these latter 
being shaped to embrace between them the revolving armature. 
The field coils are wrapped about these limbs, or magnet cores. 
In the simplest form of generator, as shown in Fig. 273, there are 
but two magnet cores and the machine is designated as bipolar. 
If there be more than one pair of cores, the machine is multipolar. 
Whatever be the number of poles, they are alternately north and 



444 



ELEMENTS OF ELECTRICITY. 



south. Fig. 272 represents the frame of a multipolar generator 
of six poles. It will be seen that a similar arrangement would 
result by grouping around a common center six horseshoe mag- 
nets, the like poles of adjacent magnets being side by side. 




Fig. 272. 

The magnet cores are made of soft annealed steel so as to be 
free from hysteresis. They are frequently laminated so as to 
avoid eddy currents. They terminate in soft iron pieces, shoes, 
which perform several functions, (a) They hold in position the 
field coils after these latter have been slipped over the cores, (b) 
They diminish the air gap between the pole faces and the armature 
core, (c) By the shape of their ends, or horns, they produce an 
advantageous distribution of the flux. 

5&2. Excitation of Field Magnets. — For all D. C. generators the 
field magnets are self-excited, that is, they are excited by current 
from the machine itself. 

Since the machine will not generate a current unless the field 
be excited, and since the field is excited by the current drawn from 



ELECTRO-MECHANICS. 



445 



the machine itself, it is not clear at first sight why a generator 
ever produces a current. If the field magnets were of perfectly 
pure soft iron, it is probable that no current would be produced 
when the generator was set in motion, but the iron is not per- 
fectly pure and there is always some slight residual magnetism 
left in the cores (Par. 155), and when the machine is started, 
this is sufficient to produce a small current through the field 
coils. This strengthens the magnets which in turn increases the 
current, and so on, a generator on starting "building up" grad- 
ually, and frequently taking a minute or so to reach normal out- 
put. This building up may sometimes be aided by the earth's 
field. 

563. Methods of Self-Excitation. — There are three distinct 
ways in which the coils of the field magnets may be wound and 
the exciting current passed through them so as to obtain the 
desired number of ampere turns. The corresponding generators 
are said to be series wound, shunt wound, and compound wound 
respectively. 

In a series-wound generator, the entire current passes through 
the field coils. In Fig. 273, a represents diagrammatically a 




»= 



FIELD 



Fig. 273. 



series-wound, bipolar machine. The same current which passes 
through the field coils flows through the external circuit, or the 
field coils and the external circuit are in series. A still more 
highly conventionalized diagram of the same machine is repre- 
sented in b. 

In a shunt- wound generator, only a portion of the entire current . 
from two to ten per cent, is passed through the field coils. These 
coils are therefore in shunt with the external circuit. In Fig. 274, 



446 



ELEMENTS OF ELECTRICITY. 



a represents a shunt-wound, bipolar machine, the shunt being 
indicated by the dotted line, and b is a more conventionalized 
diagram of the same machine. Since only a fraction of the entire 
current passes through the field coils, in order to secure the neces- 
sary ampere turns for the excitation of the magnet cores, there 
must be many more turns in these coils than in the case of those of 
a series-wound machine. 




Fig. 274. 

The field coils of a compound-wound machine combine series 
and shunt windings. Thus in Fig. 275, a represents a compound- 
wound, bipolar machine, the series winding being shown by the 
heavy line and the shunt winding by the dotted line. For clearness 
of the diagram, the windings are represented as on separate por- 
tions of the cores. 

SHORT SHUNT 




wmv^ 



LON^ SHUNT ** 
3 



Fig. 275. 

There are two varieties of the compound windings, known as 
compound short shunt and compound long shunt. If the shunt is 
taken off across the brushes A and B, as shown in a and more 
diagrammatically in b, it is a short shunt. If, as shown in c, one 
end of the shunt be taken off beyond the series coil, it is a long shunt. 
The diagrams b and c indicate the reason for these names. So far 



ELECTRO-MECHANICS. 



447 



as the machine itself is concerned, there is but little difference 
between long and short shunt, but, as will be shown in the next 
chapter, there is a very great difference in the three classes of 
machines and in the conditions under which each is to be used. 

In the foregoing diagrams the yoke of the field magnets is 
represented as above the armature, but this is simply for clearness. 
While they may have any position, bipolar machines are usually 
mounted with the yoke horizontal and below the armature, or, 
less frequently, with the yoke vertical and to one side. 

564. Control of Field. — In connection with this subject, refer- 
ence should be made here to control of field. Since the E. M. F. 
developed in a generator varies with the rate of cutting of lines of 
force, if the field be constant, the E. M. F. can be varied only by 
varying the speed of rotation. Since, however, generators are 

RHEOSTAT 




FIELD 
COILS 



Fig. 276. 

usually run at a constant speed, the E. M. F. is varied by increasing 
or decreasing the number of lines of force, that is, by varying the 
field. In a shunt- wound machine, the current through the field 
coils, and consequently the field, may be varied by means of a 
rheostat in series in the shunt circuit, as shown in Fig. 276. In a 

-X X X X 




GENERATOR 



Fig. 277. 

series-wound generator, the field may be varied by a rheostat in 
parallel with the field coils as shown in Fig. 277. The greater the 
current through the rheostat, the less through the field. These 



448 



ELEMENTS OF ELECTRICITY. 



field rheostats are not attached to the generator direct but are 
mounted upon a switchboard, an auxiliary piece of apparatus which 
will be described later (Par. 579). 

565. Armature Core. — In Par. 560 we saw that the enlarged 
portion of the shaft to which the rotating coils are attached is 
called the armature core. This core has two separate functions to 
perform, (a) It serves as a rigid base of attachment for these 
rotating coils and is therefore cylindrical in shape, (b) As ex- 
plained in Par. 145 and as shown in Fig. 182, it diminishes the air 
gap between the poles, thereby reducing the reluctance in the 
magnetic circuit and increasing the flux. It must therefore be of a 
highly permeable material, such as soft iron. It not only increases 
the flux but so directs it that the lines of force are most advan- 
tageously situated for being cut by the rotating coils. For ex- 
ample, in the multipolar machine shown in cross-section in Fig. 
278, if the armature core were non-magnetic, the lines of force 



tf 



\ \ \ v 





^k \> 


I « 1 


^ 




Or 


y*\V> ARMATURE CO 

O / \ i 


mm 


ifi / / ; 





would pass directly across the gaps abed and therefore would not 
be cut by the coils, but this core being of iron, the lines pass into it 
(Par. 145) as shown in the diagram and are cut by the coils as they 
rotate. 

The core being of a magnetic substance and lying between the 
poles of the field magnets, it acquires polarity (Par. 119). As it 
rotates, this polarity shifts and to avoid hysteretic losses (Par. 399) 
its retentivity should be very small, that is, it should be made of 
soft and pure iron. 

Also, since it is a conductor rotating in a magnetic field, eddy 
currents will be produced in it, and to reduce these it is laminated 
or built up of thin sheets (Par. 429). 

These sheets usually take the form of punchings. For small 
machines they may be disc-shaped and perforated with a single 



ELECTRO-MECHANICS. 



449 



hole for assembling upon the shaft, but for large machines they are 
generally segments of a circle. On the outer periphery they are 
provided with slots in which the coils are wrapped (Fig. 279) and 
on the inner there are undercut grooves by which they are as- 
sembled upon a spider which in turn is keyed to the shaft. 



,.-r-rr 5L0T5 



ARMATURE .--LAMINATED CORE 




COMMUTATOR 

SEGMENT 
INSULATION 



SHAFT 



-DUCTS FOR VENTILATION 



Fig. 279. 



Although this lamination diminishes the eddy currents it does 
not entirely obviate them and to reduce their heating effect the 
core is not built up solid but at intervals ventilating spaces are 
left. The air currents enter between the spokes of the spider and 
emerge through these ducts. 

566. Classes of Armatures. — Based upon the manner in which 
the coils are wrapped upon the core, there are two distinct classes 
of armatures, the ring wound and the drum wound, both shown 
diagrammatically in Fig. 280. Should the coil after passing 




glNGi WINDING DRUM WINDING^ 

Fig. 280. 

through a slot on the outer surface of the armature be threaded 
back through the interior of the core (Fig. 279), then again out 
through a slot and so on, in other words, should it be wrapped in 
a continuous helix around the rim of the armature, just as a wire 
might be wrapped around the rim of a wagon wheel to hold a tire 



450 



ELEMENTS OF ELECTRICITY. 



TERMINALS 




in position, it is a ring winding. On the other hand, should the 
coil, after passing through a slot, cross along a chord of the end 
of the core and return by a slot on the other side, it is a drum 

winding. 

Electrically the two 
windings do not differ 
in principle but prac- 
tically the drum wind- 
ing is used almost to 
the exclusion of the 
ring winding. 

One objection to the 
Fig. 281. . . ,. . ,, , 

ring winding is that 

the conductor of which the coil is composed must be put on by 

threading it back and forth and bending it into place. This is 

difficult with the large copper inductors now required ; moreover, 

any insulation about the coil would be injured in this process so 

that insulation has to be 

put on as the coil is 

placed in position, and it 

is difficult to fasten such 

coils rigidly. 

On the other hand, the 
coils for a drum winding 
being all alike may be 
made up on a form and 
of as heavy material as 
may be desired (Fig. 281). 
They are then wrapped 
with insulation, baked to 
expel moisture and var- 
nished. Finally they are 
packed tightly into the 
armature slots and held 
securely in position by 
wooden wedges inserted as shown in Fig. 282. As an additional 
precaution, a certain amount of banding is usually wrapped about 
the armature. 

567. The Commutator. — In Par. 556 we saw that the split ring, 
or arrangement of copper segments by which the alternating cur- 



r-VENTILATlNCi DUCT 
-WEDCnE 




Fig. 282. 



ELECTRO-MECHANICS. 



451 



rent was rectified, is called the commutator. With the increase in 
the number of coils, the number of segments also increases and 
they finally reduce to relatively thin wedge-shaped copper plates 
of the form shown in Figs. 279 and 283. In the upright portion or 
neck of these segments there are cut mortises into which the coil 
terminals are soldered. 



NECK 



^COMMUTATOR 5EGMENT 



WEDG,E 




Fig. 283. 



The commutator is the weakest point about the armature. Not 
only must the separate segments be assembled into a cylinder 
which is firmly attached to the armature shaft but they must also 
be perfectly insulated both from each other and from the shaft. 
The segments, separated by sheets of mica, are arranged in a 
cylinder, being held at one end by a hub or sleeve and at the other 
end by a wedge ring, from both of which they are insulated by a 
layer of a composition of mica and shellac. The sleeve and the 
wedge ring are drawn tightly together by means of bolts, thus 
binding the segments rigidly together, and these are then turned 
down to a perfect cylinder. 

568. Brushes. — The brushes are so named because in the earlier 
machines they were of brass wire and resembled a stiff paint 
brush. In the process of evolution these took the form (still used 
in certain machines) of brass laminae like the leaves of a book, 
then were made of copper gauze compressed into prisms. They 
are now rectangular blocks of carbon, made somewhat in the same 
manner as the carbons for arc lights (Par. 516) except that there 
is sometimes incorporated a small amount of paraffine which acts 
as a lubricant. They are held in brush holders which are provided 
with springs by which the pressure of the brushes against the 



452 



ELEMENTS OF ELECTRICITY. 



commutator may be regulated. The holders in turn are secured 
to a rocker frame by which the brushes may be shifted bodily in the 
direction of rotation of the commutator or in contrary direction. 
The object of this adjustment is explained later (Par. 570). The 
brushes must be proportioned to the current which they are to 
carry and for heavy currents, instead of being of a single large 
carbon block, each consists of a number of smaller carbons with 
separate springs. These may be compared to the finger tips of a 
hand pressing lightly upon the commutator. Should one be 
momentarily jarred away from the commutator, the others pre- 
serve a flexible contact and the circuit is not broken. It will be 
shown later (Pars. 573 and 577) that, except for one class of drum 
windings, there are required as many brushes as there are poles. 

569. The Ring-Wound Generator. — In the operation of a gen- 
erator, the current flowing through the coils gives rise to conditions 
which, since they necessitate certain minor corrections and ad- 
justments, should be thoroughly understood. On account of the 







Fig. 284. 

greater simplicity of the diagram, these are most readily explained 
by reference to the ring winding, but it must be remembered that 
this is selected merely for ease of explanation and that the majority 
of modern machines are drum wound. 

Fig. 284 represents diagrammatically a bipolar, ring-wound 
generator. In this diagram the extremities of each turn of the 
winding are represented as connected to the adjacent commutator 
segments, but in the actual machine there may be a number of 



ELECTRO-MECHANICS. 453 

turns between these tapping wires (see Fig. 286). The lines of 
force of the field, as shown by the dotted lines, follow around the 
rim of the armature core and therefore as the armature rotates, 
only the outer portion of the coils cuts these lines, the remaining 
portion being idle. These outer portions, the inductors, are per- 
pendicular to the plane of the paper but, in order that they may 
be seen, are shown as part of the helical winding. 

Assuming the rotation of the armature to be clockwise, applica- 
tion of the right hand rule (Par. 422) shows that the direction of 
the induced E. M. F. in each inductor to the right of the sym- 
metrical plane through the axis of the armature is from the ob- 
server, while that in each inductor in the left half is towards the 
observer. Beginning at the bottom inductor on either side and 
following around to the top, the instantaneous value of the E. M.F. 
being generated in each, assuming the field to be uniform, is 
proportional to the sine of the angle through which it has turned 
from the symmetrical or neutral plane (Par. 552), and these 
inductors being portions of a continuous helix, the total E. M. F. 
in each half of the armature is the sum of these separate E. M. F.s. 
If, therefore, brushes be applied at A and at B, the two segments 
lying in the neutral plane, and be connected through an external 
circuit, A being at a higher potential than B, a current will flow 
out by A and returning by B will divide, one-half flowing up each 
side of the armature and reuniting at A. In other words, the 
halves are in parallel and afford two paths for the current through 
the armature. An analogous arrangement would be the grouping, 
shown at the right of Fig. 284, of sixteen cells, two in parallel and 
eight in series, the variation in the E. M. F. of the individual cells 
being indicated by the length of the lines representing the cells. 

570. Armature Reaction. — The tendency of the field magnets 
of a generator is to magnetize the armature core by induction. 
As shown in Fig. 285, a north pole would be induced at N' and a 
south pole at S'. However, when the generator is in operation, 
each half of the ring core is surrounded by many ampere turns and 
is therefore powerfully magnetized. With clockwise rotation the 
current in the armature alone would produce a north pole at A T " 
and a south pole at *S"' (Par. 404). The actual magnetization of 
the ring is therefore the resultant of these two, and a north pole 
will be found at some intermediate point as N f " and a south pole 
at S'". As a result of this reaction between the original field and 



454 



ELEMENTS OF ELECTRICITY. 



the armature field, the flux will be distorted as shown and the 
neutral plane will no longer coincide with the symmetrical plane 
but will be shifted forward in the direction of rotation to some 
such position as CC. The brushes must now be shifted forward 
until they coincide with this plane, or are even very slightly ahead 
of it (Par. 572). This adjustment is made by means of the rocker 
frame (Par. 568). The plane in which the brushes are finally 
placed is called the commutation plane and the angle between this 
and the symmetrical plane is called the angle of lead. 




Fig. 285. 



The advancing of the brushes and variations in the current 
through the armature may cause further shifting of the plane of 
commutation, but generators are now so constructed that when 
the brushes have once been adjusted and the machine is run under 
average conditions, no further movement is needed. 

571. Commutation. — Fig. 286 represents diagrammatically a 
portion of the armature of a ring-wound generator in four suc- 
cessive positions. For clearness of diagram, the brush is drawn 
below the commutator segments. The broken and dotted vertical 
line represents the neutral plane. With clockwise rotation and 
field from left to right, currents will flow through the coils in the 
direction indicated by the arrows. 

In position a, the brush is in contact with segment G alone. Of 
the total current delivered to the brush, one-half flows in from the 
coil C, the other half from the coil B. 



ELECTRO-MECHANICS. 



455 



In position b, the armature has moved until the brush, still 
retaining contact with G, has just established contact with F. As 
before, one-half of the total current flows in from C, but the other 
half, arriving from A, divides at F, a small but rapidly increasing 
portion flowing direct to the brush, the diminishing remainder 
flowing through B to G and thence to the brush. The reason why 
at first only a small portion flows direct from F to the brush is 
that F is then in contact with the brush along a narrow strip only 
and the resistance of this contact is considerable. However, as 
the armature continues to move, this resistance decreases and the 
current through F increases, that through B decreasing accord- 
ingly. 




Fig. 286 



In position c, the brush makes equal contact with F and G, one- 
half of the current flows through CG, the other half through AF, 
and the current in B is zero. 

In position d, the contact with F has increased and that with G 
has dwindled to a narrow line. At this instant, the full current 
from A flows through F, while the current from C, for reasons 
explained above, divides at G, a diminishing portion flowing 
through G direct to the brush, an increasing portion flowing 
through B to F. 

When finally the brush is in contact with F alone, the conditions 
are as represented in a, that is, one-half of the total current flows 
from A to F, the other half from B to F. Originally the current 
in B flowed from left to right and it now flows from right to left, 



456 ELEMENTS OF ELECTRICITY. 

in other words, as the successive segments slip past the brush, the 
current in the corresponding coils undergoes complete reversal. 

When these changes of the current in the coil under the brush 
take place as outlined above, the commutation is said to be perfect. 

572. Sparking. — There are certain conditions which interfere 
with the realization of perfect commutation. The armature 
revolves at high speed and the reversal of the current in a coil 
often takes place in less than one-hundredth of a second. As 
these coils frequently carry from fifty to one hundred amperes 
and are wrapped about an iron core, the self -induced E. M. F. is 
considerable. The effect of this E. M. F. is to oppose any change 
in the original direction of the current flowing in the coil, therefore, 
in position d in Fig. 286 the rise of the current from G into B is 
retarded and the greater part of the current from C is forced to 
flow from G direct into the brush. As the area of contact between 
the brush and G decreases, the current density (number of amperes 
per square centimeter of cross-section) may become so great as to 
produce injurious heating of the brush and of the commutator 
segments. Finally, as G separates from the brush, a momentary 
arc is produced, its heat being sufficient to volatilize a small 
portion of both the segment and the brush. Continuance of this 
''sparking" will injure or destroy the commutator. 

If the brush be moved slightly forward in the direction of 
rotation of the armature (as for example under coil C in position 
d), the act of commutation will occur, not with a coil which is in 
the neutral plane but with one in which there is being induced an 
E. M. F. opposite in direction to the self-induced E. M. F. This 
induced E. M. F. therefore opposes and assists in overcoming the 
self -induced E. M. F. and removes this source of sparking. Gen- 
erator brushes, therefore, are usually set slightly in advance of the 
neutral plane. 

573. Multipolar Generators. — Fig. 287 represents diagram- 
matically a four-pole ring-wound generator. Application of the 
right hand rule shows that with clockwise rotation the direction 
of the induced E. M. F. is as represented by the arrowheads. If 
these be examined, it will be seen that the E. M. F. acts from the 
coils to the commutator in two points, A and B, and from the 
commutator to the coils in two other points, C and D. Therefore, 
if brushes be applied at these four points and be connected through 



ELECTRO-MECHANICS. 



457 



an external circuit, currents will flow out from A and B, and 
return by C and D. With a six-pole machine six brushes are 
needed and in general in ring-wound generators as many brushes 
are required as there are poles. Brushes of like polarity are usually 
connected to a common conductor, a ring, to which in turn the 
corresponding lead is attached. 

574. Advantages of Multipolar Machines. — Multipolar ma- 
chines possess some important advantages over bipolar machines 
and most modern machines of appreciable power are of this type. 

(a) When a coil of the generator represented in Fig. 287 has 
rotated geometrically through 180°, it has rotated electrically 




through 360°. With a six-pole machine, one-third of a revolution 
carries it through 360° electrically. Therefore, with the same 
number of lines of force from pole to pole, the same E. M. F. may 
be developed by a four-pole machine with an angular velocity 
only half as great as that of the bipolar machine. Or, if the 
angular velocity of the two be the same, the multipolar machine 
will develop the greater E. M. F. 



458 



ELEMENTS OF ELECTRICITY. 



(b) Examination of the figure will show that the current coming 
in to the machine divides equally between C and D and from each 
of these points has two paths to the positive brushes A and B, in 
other words, the current through the armature has as many paths 
in parallel as the machine has poles. With the same sized in- 
ductors, the resistance through the armature of a four-pole ma- 
chine is only one-fourth of that of a bipolar machine, or, with the 
same total current, the inductors of the four-pole machine carry 
only one-half the current as those of the bipolar. This is of great 
importance in generators handling large currents. 

Minor advantages of the multipolar machines are the more 
advantageous distribution of the flux and the less weight of iron 
required in the field magnets. 

575. Drum Windings. — The distinguishing feature of the drum 
winding has already been given (Par. 566). Since the coils are 
arranged with the inductors at opposite ends of a chord of the 
armature core (Fig. 280), if the induced E. M. F. in one of these 
inductors acts from front to rear, that in the other must act from 
rear to front. Hence, the principle governing all drum windings 
is that the coils must be so wrapped that the two inductors are 
never simultaneously under like poles. There are a number of 
different windings which fulfill this condition but they all belong 
to one or the other of two general classes, wave winding and lap 
winding. These will be explained below. 

576. Plane Development of Drum Winding.— There are two 
conventional ways of representing diagrammatically a drum 
winding. The first is to develop the armature by placing it 



Y 




LAP WINDING 



Fig. 288. 



WAVE WINDING 



on its side and rolling it along on a plane. Fig. 288 represents 
m simplest form such a development of a lap winding and of a 
wave winding (both incomplete), and indicates the appropriate- 
ness of these names. 



ELECTRO-MECHANICS. 



459 



Fig. 289 represents a lap winding for a four-pole generator, the 
armature carrying sixteen inductors and eight commutator seg- 
ments. The coils are composed of inductors 1 and 6, 3 and 8, 5 and 
10, etc. It will be noted that in each the two inductors are under 
different poles. Furthermore, if we begin at inductor No. 1 and 
follow the winding through, it will be seen that we pass in succes- 
sion through all of the inductors and finally return to the starting 
point; in other words, just as in the ring winding, the inductors are 
in series and the winding is a closed coil (Par. 559). 



N 



N 



^^^ 



i r— - 
'! N 




POLES 



INDUCTORS 



! COMMUTATOR &AR5 
BRUSHES 



With rotation from left to right, the direction of the induced 
E. M. F. is as indicated by the arrowheads, and by inspection the 
position of the positive brushes is readily located at segments 
3 and 7 and that of the negative brushes at segments 1 and 5. 

577. Star Development of Drum Winding. — An objection to the 
foregoing diagram is that the windings are not represented as clos- 
ing upon themselves. To remedy this, use is made of what may 
be termed a star development. If we should stand a barrel on end, 
cut all of the hoops except the one at the top, open out the staves 
from the bottom until the head rested upon the ground with the 
staves radiating like the petals of a daisy, we should have a star 
development of the barrel. Applying this to an armature, the 
commutator corresponds to the head of the barrel and the inductors 
to the barrel staves. The inductors and their connections are 
thus shown in their proper relation to the commutator segments 
and the windings close, the only distortion occurring in the cross 
connections at the back end of the armature. Such a projection 



460 



ELEMENTS OF ELECTRICITY. 



of a lap winding for a four-pole machine is given in Fig. 290. The 
heavy radial lines represent the inductors. To enable the eye to 
trace the back connections with least difficulty, these latter are 
drawn in a regular geometric pattern with salient angles. 

With clockwise rotation, the direction of the induced E. M. F. 
is as indicated by the arrowheads. If the circuits be traced, it will 
be seen that there should be four brushes and that they should be 
located as indicated in the diagram. There are, therefore, four 




Fig. 290. 



paths through the armature. For this reason, the lap winding is 
frequently spoken of as a parallel winding. It is best suited for 
the production of large currents at low voltage. 

A star projection of a wave winding for a four-pole machine is 
shown in Fig. 291. In addition to the manner in which it is put 
on, this winding differs from the lap winding in several other 
respects, particularly in requiring but one pair of brushes. The 
positions of the positive and the negative brushes are shown in the 



ELECTRO-MECHANICS. 



461 



diagram. Should an additional negative brush be introduced at c 
and connected to b, it would be of no appreciable electrical effect, 
for examination of the diagram will show that c and b are already 
connected through the coil cdeb in which, at the instant shown, 
no E. M. F. is being induced. The inductors of a wave winding 
are therefore in series and there are but two paths through the 
armature, for which reasons wave-wound armatures are best 
suited for the production of small currents of high voltage. 




Fig. 291. 



578. Calculation of E. M. F. of Generator.— The E. M. F. of a 

generator may be calculated as follows: 

Let 0=flux from each pole 
n = number of poles 
n' = number of revolutions per second 
n" = number of paths through the armature 
N = number of inductors 



462 ELEMENTS OF ELECTRICITY. 

The number of flux lines cut by each inductor in one revolution 
is n.0. 

The number of flux lines cut by each inductor per second is 
n'.n.ct). 

The E. M. F. generated by each inductor is n'. n . 0/1O 8 . 

But since there are N In" inductors in series, the total E. M. F. 

N.n'.n.<t> ,, 

is „ 1AR volts. 

n" . 10 8 

579. Switchboards. — A generator may be called upon to furnish 
current for various uses, as, for example, for lighting, for charg- 
ing a storage battery, for running a motor, etc., etc., and it may 
be required to do these things one at a time or in various com- 
binations. Wires must therefore be run from the generator to 
the lamps, battery, machines, etc., and there must be switches 
in the various circuits. The generator must be supplied with 
a field rheostat (Par. 564) by which its E. M. F. may be adjusted, 
and this implies that it must also be equipped with a voltmeter 
by which this E. M. F. may be measured. If a storage battery 
is to be charged, its E. M. F. must be known before the current 
from the generator can be turned on (Par. 245). It is also often 
desirable to know the current flowing in any one of the circuits, 
and for this there must be ammeters. Overload switches should 
be inserted in the principal circuits and an underload switch 
must be in the charging circuit for the storage battery (Par. 
415). Should an attempt be made to connect these various 
switches and instruments to the generator direct, the machine 
would be hidden in a hopeless maze of wiring. These auxiliary 
pieces of apparatus are therefore gathered together, taken to 
one side and mounted upon a switchboard. Wires from the 
machine, not exceeding three in number, are brought over in a 
conduit and the distribution of electrical energy takes place at 
the board. This distribution is usually made from two heavy, 
parallel copper bars, called bus bars, which are connected to the 
source of the electrical energy and which may be regarded as its 
enlarged terminals. 

Originally of minor consideration, the switchboard has now 
risen to a position of importance second only to that of the 
machine itself and frequently rivalling it in cost. It is composed 
of panels of some non-conducting material, preferably marble, 
upon the front of which are mounted the switches and instru- 



ELECTRO-MECHANICS. 



463 



merits; the bus bars, wiring and connections being at the back. In 
addition to a symmetrical distribution of the apparatus, it is cus- 
tomary to arrange parallel wires of a circuit on direct-current 
switchboards so that if they be horizontal, the upper one is the 
positive wire; if they be vertical, the right hand one is positive. 



LAMPS 



s ' tsm 




BARS 




STORAGE BATTERY 

Fig. 292. 



UtP 



GENERATOR 



FIELD 
RHEOSTAT 



5HUNT 
FIELB 



In drawings of switchboards, several conventions are observed. 
Wires are always drawn as right lines which are perpendicular 
or parallel to the lower edge of the board (Fig. 292). This is to 
aid the eye in tracing the circuits. If two wires cross but are not 
connected electrically, this fact may be indicated by a little arch 
in one of the wires, or they may be assumed not to make connec- 
tion unless a dot be made upon the point of intersection. 



464 ELEMENTS OF ELECTRICITY. 

580. Example of Switchboard. — A switchboard by which the 
current from a shunt-wound generator may be used to run a 
number of lamps and charge a storage battery, either separately 
or simultaneously, is shown in Fig. 292. The circuits are easily 
followed by the eye and the use of the various switches will be 
understood from the following: 

To charge the battery: 

(a) Close b to the left and read the battery voltage. 

(b) Start the generator. Close b to the right and read the 
generator voltage. Manipulate the field rheostat until 
the generator voltage is about ten per cent greater than 
the battery voltage. 

(c) Close a, c, and last the underload switch. 
To run the lights at the same time : 

Close also d. 
To run the lights separately: 

With the above arrangement open c. 
(It will be noted that the lights are now run through the under- 
load switch. This is not correct. An additional switch should 
be used by which the generator may be thrown direct on the bus 
bars. It is omitted in the diagram to avoid overcrowding the 
figure.) 

The right hand ammeter reads the current from the generator. 
To run the lights from the battery alone : 

With all switches open, close c and d. 
The left hand ammeter now reads the current from the battery. 

581. Coupling of Generators; Three- Wire System. — In Par. 
502 it was shown that the successful transmission of electrical 
power to a distance depended upon the employment of high 
voltage, the loss of power in the leads varying inversely as the 
square of this voltage. Alternating currents are easily stepped 
up for transmission and as easily stepped down at the point 
where they are to be utilized. In the case of direct currents the 
transformation is much more troublesome and expensive. For 
such currents, however, there has been devised a system by 
which the voltage may be doubled and thus the advantage of 
high voltage transmission be partly secured. This will be under- 
stood from the following explanation. It is desired to operate 
at a distance a number of 110 volt incandescent lamps. If two 



ELECTRO-MECHANICS. 



465 



generators, A and B, each capable of delivering 110 volts to the 
lamps, be connected in series as shown in Fig. 293, the voltage 
between the leads will be 220. If the lamps between C and D 
be arranged two in series, each will receive its required 110 volts, 




0000 



N 



0000 



Fig. 293. 

while the currents in the leads will be only one-half of that re- 
quired by the same number of lamps arranged singly in parallel. 
The leads therefore may be reduced three-quarters in size. If now 
a third wire NN, the neutral, be inserted as shown in the figure, 
it will be possible to have a different number of lamps on the 
two sides. If there be more lamps above the neutral than below, 
the excess current flows in on the neutral; if there be less above, 
the excess current flows out on the neutral, in other words, the 
neutral needs only be sufficiently large to carry the difference in 
the currents required on the two sides. In practice, however, 
it is made of the same size as the other two leads. Notwithstand- 
ing the extra wire, the saving in copper in this three-wire system 
is five-eighths, or 62.5 per cent, of the amount required in a two- 
wire system for transmitting equal power. Against this saving 
must be put the cost of the extra generator (though certain special 
generators have been devised to supply a three-wire system 
from a single machine), and the extra cost of installation and of 
switches and switchboard appliances, so that frequently the 
saving is more apparent than real. In addition to this, more 
attention is required in regulating the two generators since with 
unequal loads on the two sides of the neutral, the E. M. F. of 
the generators must differ. 

The principle involved has been applied abroad to a five-wire 
system. 



466 ELEMENTS OF ELECTRICITY 



CHAPTER 41. 

GENERATOR CHARACTERISTICS. 

582. Adaptation of Generator to Work Required. — Of the vari- 
ous proposed classifications of direct current generators, the 
most important is the one based upon the excitation of the field 
magnets (Par. 563), that is, into series, shunt and compound 
machines. 

Each one of these classes possesses certain advantages and 
disadvantages which render it more suitable for some purposes 
and less so for others. 

As an illustration, suppose we have at our disposal a series 
generator and a shunt generator and are required to charge a 
storage battery: which of the two should we use? 

To prevent the storage battery from discharging back through 
the generator, the voltage of the latter must be kept constantly 
higher than that of the battery. Suppose we were to start with 
the series generator. Its E. M. F. can not build up until a 
current flows through the field coils, and no current can flow 
through these until the external circuit is completed. There- 
fore, should we simply start the generator and then switch it 
on to the storage battery, the battery would discharge back 
through the generator. We must then first build up its field 
by sending the current through some external circuit other than 
that which includes the battery and then, when the E. M. F. 
has reached the proper point, switch the current in on the 
battery. 

Suppose this to have been done and that the connections are 
as shown diagrammatically in Fig. 294. As the battery becomes 
charged, its voltage rises, consequently the current sent through 
it by the generator grows smaller. The current through A B 
being smaller, the field gets weaker: the voltage of the generator 
consequently falls; this again causes the current to decrease; 
the field gets still weaker, and so on. In other words, the generator 
unbuilds and "drops its load," and, unless there be an under- 
load switch in the circuit, the battery will soon discharge back. 



ELECTRO-MECHANICS. 467 

A series-wound generator is therefore not fitted to charge a stor- 
age battery. 

/«FHiHi \M*~ 

(\ FIELD BATTERY 



Fig. 294. 

On the other hand, suppose that we employ the shunt generator 
and that it is connected as shown in Fig. 295. The generator is 
started and, the current flowing through the shunt field AB, 
the E. M. F. builds up rapidly. When the voltage has reached 
the proper point, the switch S is closed and the current is thrown 
in on the battery. As the battery becomes charged, its voltage 
rises and this counter E. M. F. cuts down the current from the 
generator but the effect is very different from that in the case 
of the series generator. As the current from the shunt generator 
decreases, its voltage increases. The explanation of this is as 
follows. The E. M. F. of the generator at any instant is spent 



Fig. 295. 

in doing two things, driving the current through the resistance 
of the armature coils and brush contacts (or through the internal 
resistance of the machine), and driving it through the resistance 
of the external circuit, including the overcoming of any counter 
E. M. F. in that circuit. This will be recognized as but another 
example of lost and useful volts as discussed in Par. 305. The 
smaller the current through the armature, the smaller the lost 
volts, or the internal drop Ir, and the more nearly the voltage 
between A and B approaches the E. M. F. of the generator. 
We see then that the voltage of the shunt generator always re- 
mains greater than that of the battery and that the charging can 
be done with safety. 



468 



ELEMENTS OF ELECTRICITY 



583. Characteristics. — The advantages and disadvantages of 
the various forms of generators may be discussed in a similar 
manner to the foregoing. Where constancy of current is to be 
maintained, a series generator is under certain conditions satis- 
factory; where constancy of voltage is desired, a shunt or a 
compound generator must be employed. However, we might 
sometimes overlook some point in our discussion or might give 
undue weight to some other, therefore, the most sure method 
is actually to try the machine under varied conditions, keep a 
record of the results, tabulate and compare these. If they can 
be put graphically in the form of a curve, they give a clearer 
conception of the working of the machine. Such curves are called 
"characteristics" and much information can be derived from their 
study. 

584. Magnetization Characteristics.— As an illustration of these 
characteristics, suppose that we have a generator whose field is 




Fig. 296. 

excited from a separate source, such as a storage battery. We 
rotate the generator at a constant speed, we excite the field by 
various currents and we record the strength of the exciting cur- 
rent and the corresponding voltage across the brushes of the 
generator. Plotting this data with amperes as abscissae and the 
corresponding volts as ordinates, we obtain a curve (Fig. 296) 
which is called the "magnetization characteristic." 

A study of this reveals (a) that with no current in the field 
coils there is still a small voltage, OA, due to the residual magnet- 
ism of the magnet cores (Par. 562), and (b) that as the amperes 
in the field coils increase regularly, the voltage at first rises rapidly 



ELECTRO-MECHANICS. 



469 



and then more slowly. Reflection will show that this curve is 
nothing more than the magnetization curve described and figured 
in Par. 393. 

585. Characteristic of Series Generator. — Fig. 297 represents 
diagrammatically a series generator run at constant speed and 

FIELD 




AMMETER 

Fig. 297. 

connected in circuit with a number of lamps in parallel and an 
ammeter. A voltmeter is connected across the terminals. By 
turning on lamps the resistance of the circuit is reduced and the 
current thereby increased. This current is measured by the am- 
meter and the corresponding terminal voltage is given by the 
voltmeter. If the amperes be laid off as abscissae and the cor- 
responding volts as ordinates, the resulting curve, ABM N, Fig. 
298, is the external characteristic, so called because, as was pointed 































-H 




I 










„. 


--' 


- " 




























s " 




M, 




























/^ 






/ 




















N 








1 


/ 






/ 






























I 1 

I I 






i 


/ 






























If 






/ 






























/ 
1 






/ 






























r 


II 




/ 
t 








































































I 


'. 




































f/ 







































K D AMPERES 

Fig. 298. 

out above (Pars. 461 and 582), the voltage read by the voltmeter 
is not the total E. M. F. of the machine but only the IR drop 
over the external circuit, in other words, the useful volts. Should 
we wish to represent the total E. M. F., the internal drop, or 
lost volts Ir, must be added to the external drop. 



470 ELEMENTS OF ELECTRICITY. 

Since r, the internal resistance of the machine, is constant, 
the internal drop varies directly as the current and is represented 
in Fig. 298 by the straight line OF. If the ordinates of OF be 
added to the corresponding ordinates of the curve ABMN, the 
resulting curve OH is the total E. M. F. curve or the internal 
characteristic. Were it not for the effects of armature reaction, 
this curve would agree with the magnetization curve described 
in the preceding paragraph. 

Examination of the external characteristic shows that the 
machine should be operated with currents corresponding to the 
flatter portion of the curve, for if the current falls below KO, 
slight changes in the current produce great fluctuations in the 
voltage and the operation of the machine is unstable. 

586. Critical Resistance. — From the figure, MD/DO is the 
tangent of the angle MOD, and since MD represents E. M. F. 
and OD represents current, E/I = tan 0. But from Ohm's law 
E/I = R, hence, at any point upon the external characteristic 
the corresponding external resistance is proportional to the tan- 
gent of the angle which the ordinate at that point subtends. 

As the external resistance is increased, the angle 6 increases 
and the point M moves towards B. Finally, a very slight in- 
crease in 6 will cause M to drop to the origin. There is therefore 
for a series generator an external resistance, the critical resistance, 
beyond which the generator will not operate. Reflection will 
show the correctness of this conclusion since the resistance must 
always be small enough to permit a sufficient current to flow 
through the field coils and produce the necessary strength of field. 

587. Characteristic of Shunt Generator. — If a shunt gener- 
ator be connected up as shown in Fig. 299 and data be obtained 



B AMMETER 1N 

Fig. 299. 

and characteristic plotted as described in Par. 585, the resulting 
curve (Fig. 300) will be seen to differ widely from the one obtained 
from the series machine. To begin with, the voltage is a maximum 



ELECTRO-MECHANICS. 



471 



when there is no current in the external circuit. As the current 
is increased, the voltage falls quite regularly until a final point is 
reached when a further decrease in the external resistance causes 
both the current and the voltage to drop and if all resistance be 
removed, the machine unbuilds entirely and the curve returns 
upon the origin. 















































































































































































\ 


\ 






































































J 


I 


































y 








o 

> 






















































































































Ar 


1P 


ER 


IS 



















Fig. 300. 

The foregoing results are brought about by two causes. First, 
the current through the shunt grows smaller and the field con- 
sequently weaker. Whatever decreases the difference of potential 
between A and B (Fig. 299) decreases the current through the 
field coils. With no current in the external circuit, the full E. M. 
F. of the machine is available for driving current through the 
shunt. When, however, a current flows through the armature, 
the available E. M. F. is the total E. M. F. diminished by the 
internal drop, Ir, which last varies directly with the current. 
At first, as the field current weakens, the voltage is not greatly 
affected since the field magnets are being worked on the upper 
part of the magnetization curve. When, however, the magnet- 
ization falls below the bend of the curve, it drops rapidly as the 
exciting current decreases. 

Second, the field is weakened by the armature reaction. Con- 
sider the diagram (Fig. 301) of the drum-wound bipolar machine. 
With clockwise rotation, the brushes will be shifted from the 
symmetrical plane to the positions A and D (Par. 570). In the 
inductors in the semi-circumference ABCD, the current is flowing 



472 ELEMENTS OF ELECTRICITY. 

in; in the other semi-circumference it is flowing out. The effect 
of the current in the inductors C to D and A to F is to produce a 
field in the direction of the large arrow, that is, opposite to the 
field of the magnets and consequently weakening that field, and 
this effect increases as the current through the armature increases. 




Fig. 301. 

For this reason, the ampere turns between C and D and between 
A and F, or in the double angle of lead, are named the demagnet- 
izing turns. 

The critical resistance for a shunt generator is that resistance 
of the external circuit which if reduced will cause the machine 
to unbuild. 

588. Compound Generator. — The properties desired of a gener- 
ator vary in accordance with the use to which the current is to 
be put. In some circumstances constancy of current is required; 
in others, constancy of potential. Of these, the more important, 
notably in the case of electric lighting (Par. 511), is constancy of 
potential. Neither the series nor the shunt generator afford this 
desired constancy. However, we have shown above that the 
voltage of a series generator rises as the current is increased, 
while that of the shunt machine falls with this increase. The 
logical attempt to combine these windings in one machine so that 
their effects counterbalance, has led to the development of the 
compound generator. This compounding may be so carried out 
that the voltage, even under wide fluctuations in the current, 
remains nearly constant. 

589. Overcompounding. — If in a compound machine the series 
coils be given a few more turns than are needed to preserve con- 
stant potential, the voltage rises with increase of current, although 



ELECTRO-MECHANICS. 473 

not so rapidly as in the case of the simple series machine. The 
generator is then said to be over compounded. The object of over- 
compounding will be understood from the following. Let G, Fig. 
302, represent a compound generator supplying current to a dis- 

1 OHM 





B 1 OHM 

Fig. 302. 

tant group of lamps CD. Suppose each lamp to require one 
ampere at 100 volts and suppose the resistance of the leads AC 
and BD to be each one ohm. When one lamp is turned on, there 
is a drop of one volt from A to C, and of one volt from D to B. 
In order therefore that the voltage between C and D shall be 100, 
the generator must develop between its brushes 102 volts. If all 
five lamps be turned on, there will be a drop of five volts from 
A to C, and of five from D to B; the generator must therefore 
develop between its brushes 110 volts. We see then that a gener- 
ator is overcompounded so that a constant difference of potential 
may be maintained between two points at a distance from the 
generator. 



474 



ELEMENTS OF ELECTRICITY. 



CHAPTER 42. 

DIRECT CURRENT MOTORS. 

590. The Motor and the Generator Identical. — An electric 
generator, as we have already seen, is a machine to which 
mechanical energy is applied and from which electrical energy 
is drawn; on the other hand, an electric motor is a machine to 
which electrical energy is applied and from which mechanical 
energy is derived. Electrically, they are identical, and a machine 
which if turned by mechanical power will produce a current, 
will, if supplied with a current, develop mechanical power. The 
truth of this statement may be shown by the following simple 
illustration. Fig. 303 represents the arrangement, already de- 




scribed several times, of a wire sliding on parallel conducting 
rails which include between them a magnetic field. The wire AB 
is a conductor in a magnetic field and if pulled in the direc- 
tion C, there will be induced in it a current from A to B (Par. 
422) ; it is therefore a generator in its simplest form. If instead 
of pulling the wire, a current be passed through it from A to B, 
it becomes a conductor carrying a current and placed in a magnetic 
field and experiences a force (Par. 356) which will cause it to 
move in the direction D (Par. 352); it is therefore also a motor. 

591. Explanation of Motion. — Let AB, Fig. 304, represent a 
coil of wire placed in a magnetic field NS and free to revolve 
about the axis CD. If a current be sent through this coil it will 
start to rotate. The simplest explanation of this motion is that 
each side of the coil is a conductor carrying a current and placed 



ELECTRO-MECHANICS. 



475 



in a magnetic field and is therefore acted upon by a force which 
is at right angles to the field and whose strength is (Par. 356) 

f = I. H .1 dynes 

In this expression / is the current in absolute units, H is the 
strength of the field, or number of lines of force per square centi- 
meter, and I is the length in centimeters of the wire at right angles 




Fig. 304. 



to the field. The direction of the current in one side of the coil 
being opposite to that in the other, the force acting upon one side 
is opposite to that acting upon the other; in other words, the two 
forces constitute a couple and rotation will be produced. Its 
direction may be determined by applying the left hand rule (Par. 
352). 

The following additional explanation of this movement is given 
as it involves certain conceptions which will be used in a discus- 
sion later on. 

The lines of force of the field run from AT" to S as shown by the 
heavy arrow. If a current enters the coil by A and leaves by B, 
there will be produced within the coil a field whose direction, as 
shown by the broken arrow, is from above downward. In ac- 
cordance with Maxwell's law (Par. 371), the coil will turn until 
it embraces its own field and that of the magnet; it will therefore 
take up a counter-clockwise rotation. The turning effect of the 
couple mentioned above becomes zero when the coil has revolved 
until it lies in the vertical plane, and is reversed when the coil 
passes through this plane. The coil would therefore come to rest 
in this position. However, by means of a suitable commutator, 



476 ELEMENTS OF ELECTRICITY. 

as explained under generators (Par. 556), the current is reversed 
as the coil passes through the vertical plane; its field is therefore 
shifted 180° ahead and the rotation becomes continuous. More- 
over, by using many coils upon the armature (Par. 558), it is 
always possible to have the current flowing through those in 
which the turning effect is at or near a maximum. 

592. Power Developed by a Motor. — Power is the rate at which 
work is done (Par. 492), therefore 

t. work 

Power = — - — - 

time 

Work is force exerted over a path, hence 

Power = forCeXpath 

time 



force X 



path 



time 
= force X velocity 

Consider one of the inductors of the armature of a motor (Fig. 

^ c 305). The force exerted upon it is (Par. 591) 

/="/ . H . I dynes. An equal force is exerted 
upon the inductor diametrically opposite. 

If r be the radius of the armature, in one 
complete revolution the inductor travels a dis- 
tance 2irr. In n revolutions it travels 2irrn. 

If these n revolutions be made in time t, the 
velocity with which the inductor travels is 

rig. ouu. 

2irrn/t. 
From above, power = force X velocity, hence power developed 
by the motor is 

P=2IHlx2irrn/t 

This may be written 

P = IHlx2rX 2im/t 

But IHlx2r= armature moment = torque, and 2-n-n/t = angular 
velocity of the armature, hence the power developed varies with 
the torque and with the speed of rotation of the armature. 

593. Counter Electro -Motive Force. — Ignoring for the moment 
the cause of the movement, consider a rectangular coil, as de- 
scribed in Par. 591, rotating in a counter-clockwise direction in 



ELECTRO-MECHANICS. 



477 



a magnetic field. The sides of this coil are conductors moving in 
a magnetic field. Application of the right hand rule (Fig. 306; 
will show that there is induced in the coil an E. M. F. which acts 
in at B and out at A. The more rapid the rotation, the greater 
this E. M. F. (Par. 425). Comparing figures 306 and 304, we see 




that this E. M. F. is opposed to that of the current which causes 
the motor to rotate; in other words, the rotation of the motor sets 
up an E. M. F. which opposes the current which produces the 
rotation. This opposing E. M. F. is called the counter or back 
E. M. F. 

The first conspicuous effect of the counter electro-motive force 
developed by a motor is to cut down the current supplied. If an 
ammeter be connected in series with a motor and the circuit be 
closed, it will be noted that before the motor begins to move, the 
current is very large (indeed, without some special arrangement 
to be described later [Par. 601] it may be excessive), but as the 
motor speeds up, the current falls steadily. 

If the E. M. F. applied to the brushes of a motor be E, and the 
resistance of its armature be R, the current through the armature 
before the motor moves is 

1 R 

and as R is small, / is great. 
As the motor gains speed, the current becomes 

T — E — Eb 
1 " R 



478 ELEMENTS OF ELECTRICITY. 

or only so much as can be driven through the armature by the 
difference of the impressed and the back E. M. F. 

594. Relation Between Counter E. M. F. and Power Developed. 

— Since the power which a generator delivers to the brushes of a 
motor is IE watts (Par. 494), and since, as shown above, I is cut 
down by the back E. M. F. developed and hence the power re- 
ceived by the motor is thereby diminished, it would seem that 
back E. M. F. is a defect. However, consider the following: 

From above, the current which a generator supplies to a running 
motor is 

1 = 



E — E b 



R 

whence IR = E — E B 

whence PR = IE- IE B 

whence IE = PR + IE B 

or IE, the total 
power delivered to the motor by the generator, is divided into two 
parts, one of which, PR, represents power lost in heating the 
armature coils (Par. 494); the other, IE B , represents the useful 
power of the motor. Hence, the useful power of a motor is direct- 
ly proportional to the back E. M. F. which it develops. 

From the foregoing, the useful power of a motor varies with the 
product of the two factors I and E B . In Par. 592 it was shown 
that this power also varies with the product of two other factors, 
the torque and the speed of rotation. The torque, / . H . I X 2r, 
if the field H be constant, varies directly with the current I, con- 
sequently, the remaining factor, E B , the counter E. M. F., varies 
directly with the speed of rotation. This might have been antici- 
pated since we have shown above that the counter E. M. F. varies 
with the rate at which the lines of force of the field are cut. 




Fig. 307. 

595. Reading of Voltmeter Across Seat of Counter E. M. F. — 

There is sometimes some confusion in the mind of a beginner as 
to the reading of a voltmeter shunted around a seat of counter 
E. M. F. The correct reading is always the sum of the counter 



ELECTRO-MECHANICS. 479 

E. M. F. and of the regular IR drop over the resistance between 

the two points. As an illustration, let G, Fig. 307, represent a 

generator connected up in circuit with a motor M across whose 

brushes a voltmeter is shunted, Let the E. M. F. of the generator 

be 100 volts and suppose its resistance to be negligible. Let the 

resistance of the leads be one ohm and that of the motor be one 

ohm. Suppose that the generator is started but that the motor 

is held fast and not allowed to rotate. The current is I = E/R = 

100/2 = 50 amperes. The drop over the leads is IR = 50 volts 

and that across the motor is Ir = 50 volts, which is the reading 

of the voltmeter. Suppose now that the motor is released and 

speeds up, producing a back E. M. F. of 90 volts. The current is 

T E-E B 100-90 K . ' ,, , ,, 

now I = — s — = ~ = 5 amperes, or is reduced to one-tenth 

ti Z 

of what it was originally. The IR drop over the leads is only 5 

volts; the reading of the voltmeter therefore is 100 — 5 =95 volts, 

that is 90 for the back E. M. F. and 5 for the Ir drop across the 

armature. 

596. Efficiency of Motors. — A generator delivers to the brushes 
of a motor a current I of voltage E. The resistance across the 
brushes is R. The motor rotates and by belts or gearing or other- 
wise turns out mechanical power. The ratio of the power turned 
out by the motor to the power delivered to its brushes by the 
generator is the measure of the motor's efficiency. Thus, if the 
generator supplies ten horse-power to the motor and the motor 
turns out nine horse-power, its efficiency is 9/10 or 90 per cent. 

The power delivered to the motor is IE watts (Par. 494); the 
useful power turned out by the motor is IEb watts (Par. 594); 
the efficiency of the motor is therefore measured by IEb /IE or 
by E B /E; that is, the nearer the counter E. M. F. approaches the 
applied E. M. F., the greater the efficiency of the motor. 

The foregoing may be shown graphically as follows. The cur- 
rent through the motor when the latter is running is (Par. 593) 

T — ^ ~ ^ B 

1 " R 

Substituting this value of I in the above expressions, we obtain 
for the power delivered to the motor 

E{E — Eb) 
R 



480 



ELEMENTS OF ELECTRICITY 



and for the power turned out by the motor 

Eb(E — Eb) 



whence the efficiency is 



R 

Eb(E — Eb) 




E{E - E B ) 
Upon rectangular axes (Fig. 308) lay off OA=OB propor- 
D J K tional to E B , and OD =OF propor- 

tional to E. Complete the squares. 
The area of the rectangle ADJG, 
since it is proportional to E B (E — 
E B ), is proportional to the power 
developed by the motor. The area 
of the rectangle BJKF, since it is 
proportional to E(E — E B ), is pro- 
portional to the power delivered to 
the motor. The ratio of the first of 
these rectangles to the second meas- 
es- 308 - ures the efficiency of the motor. The 
rectangle BJKF is greater than ADJG by the area of the square 
JGKH. The efficiency of the motor approaches unity as this 
square diminishes, which it does as OA increases, that is, the 
efficiency of the motor increases as the counter E. M. F. increases. 
It must be noted, however, that as the counter E. M. F. OA = 
OB, increases, the current through the motor decreases, and the 
rectangles representing the power applied and the power turned 
out both diminish, therefore, so long as the motor develops ap- 
preciable power, its efficiency is never perfect. 

597. Maximum Output of Power. — Maximum efficiency must 
not be confused with maximum output of power. From the pre- 
ceding paragraph, the power turned out by the motor is 

Eb(E — Eb) 



z = 



R 



watts 



The first differential coefficient with respect to E B is 

2E B ) 



dz 1_ F 
dE B R K 



Placing this equal to zero and solving for Eb 

1 



E 1 



E 



ELECTRO-MECHANICS. 481 

or the power turned out by a motor is a maximum when the 
counter E. M. F. is equal to one-half the impressed E. M. F. In 
this case the efficiency is only one-half; that is, there is a loss of 
one-half of the power delivered to the motor. 

Reference to the conclusion drawn in Par. 340 will show that 
in a battery also when the power developed is a maximum, the 
loss is one-half. 

598. Classes of Direct-Current Motors. — There are three classes 
of direct-current motors, the series, the shunt and the compound. 
The majority belong to the first two of these classes. In structure 
they are, with a few minor changes, the same as the correspond- 
ing generators. Thus, the requirement of being able to reverse 
the direction of rotation at will involves the setting of the brushes 
at right angles to the commutator surface instead of inclined there- 
to. So also in the operation of a motor, the armature reaction 
causes the brushes to be shifted backward from the neutral plane 
instead of forward as in the case of the generators. 

As a rule, motors are operated on constant potential circuits, 
the voltage between the mains being constant. 

599. Shunt Motors. — The shunt motor possesses certain ad- 
vantages over the other forms which render it by far the most 
desirable for most mechanical purposes. Chief among these is 
its ability, as shown below, to make automatic adjustment for 
fluctuations in the load thrown upon it and in spite of these 
fluctuations to vary but little in speed. 

s 




Fig. 309. 

Fig. 309 represents in simplest diagrammatic form a shunt motor. 
The difference of potential between A and B being constant, as 
stated above, the current through the field coil AB is constant. 

The force on the several inductors of the armature is (Par. 592) 
f = I. H . I dynes 

In this expression H and I are constant, hence the torque varies 
directly with the current through the armature. In order there- 
fore to vary the torque for different loads, this current must vary. 



482 ELEMENTS OF ELECTRICITY. 

The current through the armature is (Par. 593) 

j _ E — Eb 
R 

From this we see that the current can be increased by increas- 
ing E, decreasing Eb, or decreasing R. Now E is the voltage 
between the mains, which we have seen above is constant, and R 
is the armature resistance, which is fixed when the machine is 
built. The only remedy therefore is to decrease E B , the back 
E. M. F. This back E. M. F. varies with the rate at which the 
lines of force of the field are cut (Par. 594), that is, it varies 
directly with the speed of rotation. 

When the load upon a shunt motor is suddenly increased, the 
speed will be observed to decrease slightly. This does not mean 
that the machine is weakening. On the contrary, by slowing 
down, the back E. M. F. is decreased, the current and hence the 
torque increase. 

A numerical example will bring this out clearly. If in the above 
expression for the current we make £' = 110, Eb = 100 and R = l, 
we get 1 = 10 amperes. If we make E B = 90, I becomes 20 
amperes, hence a reduction of one-tenth in the speed of rotation 
doubles the torque on the armature. 

Since the power developed by the motor is IE B (Par. 594), 
it may be asked whether the increase in I were counterbalanced 
by the decrease in Eb, for if they varied reciprocally, the power, 
IE B , might remain constant and nothing would be gained. 
However, I increases in a more rapid ratio than E B decreases. 
In the numerical example above, with £5 = 100, the power is 
1000 watts; with E B = 90, the power is 1800 watts. 

The valuable characteristic of the shunt motor therefore is 
that by slight variations in speed it adjusts itself automatically 
for wide variations in the load. Even should the load be suddenly 
entirely taken off, the motor will not "race," or speed up danger- 
ously. 

600. Control of Speed of Shunt Motors. — The speed at which 
a shunt motor runs under a certain load may be controlled in one 
of two ways. The first and most frequently employed method is 
by varying the strength of the field. There is inserted in the field 
circuit a rheostat by which the current through the field coils may 
be varied. By increasing the resistance in this circuit, the field 



ELECTRO-MECHANICS. 483 

H is weakened. This causes E B to dimmish and the current 
through the armature consequently increases. The torque, I Hlx 
2r (Par. 592), is thus increased and the machine speeds up. It is 
true that the torque depends also upon H, but we have shown in 
the preceding paragraph that / increases more rapidly than H 
decreases. This increase of speed also follows from the fact that 
if the field be weakened, the armature must revolve faster in 
order to cut the same number of lines of force in the same time 
and thus develop the same power. 

The second method is to insert between the motor and one of 
the mains, as shown in Fig. 310, a rheostat R. The field H is not 




:ro •. 



c 






^J 



B 



Fig. 310. 

affected by this, but the voltage applied to the armature is the 
total voltage between A and B less the drop over the rheostat. 
By varying the resistance in R, and hence the drop across the 
rheostat, the voltage between C and B, and hence the current 
through the armature, may be varied. Since the torque, I Hlx 
2r, H remaining constant, varies directly with /, a decrease in 
the current decreases the speed of rotation. 

From the foregoing it is seen that the speed of a shunt motor 
may be increased (a) by decreasing the current through the field 
coils, or (b) by increasing the current through the armature. 

It should be remarked that control by rheostat is objectionable. 
The power consumed in heating the coils of the rheostat repre- 
sents pure waste which, where power is purchased, must be paid 
for just as if it were doing useful work. The waste in the second 
method above, since a larger current passes through the rheostat, 
is much greater than that in the first method. 

601. Starting-Box for Shunt Motors. — It was stated above, 
(Par. 593), that the full voltage can not without serious risk be 
turned on a motor at rest. It is customary to use a starting-box, 
a form of rheostat by which, as the back E. M. F. rises, the ap- 



484 



ELEMENTS OF ELECTRICITY. 



plied E. M. F. may be gradually increased. The starting-box for 
a series motor does not differ sufficiently from an ordinary rheostat 
to warrant a special description. The starting-box for a shunt 
motor possesses certain features which require explanation. 

Although for these motors the full voltage can not be applied at 
first to the armature, it can with perfect safety be applied to the 
field coils. This enables the field to attain its full strength H at 
once, and although the current I through the armature be small, 
the torque is great enough to cause the machine to gather headway 
rapidly. 

Fig. 311 represents diagrammatically a form of starting-box 
largely used. It is a box-shaped frame with lattice- work sides for 







Fig. 311. 



ventilation and contains a number of resistance coils in series 
between a set of contacts arranged along the arc of a circle on 
the marble cover of the box. The wire of the coils must be of 
sufficient size to carry the current required by the motor, and 
therefore to secure the necessary resistance they have to be long. 
An iron arm, pivoted at P, can be swept along over the contacts. 
At the pivot of this arm there is a spring which, when the arm is 
released, throws it back to the safety position. When the arm is 
placed on the first contact C, the current from the positive main 
comes in by L, thence to P, thence up the arm to C where it 
divides, a part passing through all the resistance coils to D, thence 
to A, thence to the armature of the motor and thence to the 
negative main, and the other part passing through the coil H, 
thence to F, thence through the field coils to the negative main. 
At starting, therefore, the current through the armature is cut 
down by the entire resistance of the coils from C to D, while the 



ELECTRO-MECHANICS. 485 

field is of full strength. As the armature begins to revolve it 
generates a back E. M. F. and it becomes safe to apply more 
voltage. The arm is therefore rotated to the right and gradually 
cuts out the resistance in the armature circuit. 

When the arm is hard over to the right, the entire resistance is 
out of the armature circuit and the arm is held by the electro- 
magnet H. The object of this magnet is the following. Should 
the circuit be broken or the power be turned off while the motor 
is in operation, the arm of the rheostat should be automatically 
returned to the safety position, otherwise the break might be 
repaired or the power be turned on again with the arm in its full 
load position and the armature coils be overheated or even burned 
out. When a break occurs, the magnet loses its power and the 
spring at P throws the arm back to the safety position. This 
arrangement is called a "no voltage release." 

Again, should by any accident the current through the field 
coils be greatly reduced or entirely cut off leaving only the residual 
magnetism of the field magnets, the motor, from what has been 
shown in the preceding paragraph, would speed up dangerously, 
or, if this did not occur, would not generate sufficient back E. M. 
F. to keep the current through the armature down to safe limits. 
Therefore, in this case also the rheostat arm should be automati- 
cally thrown back to the safety position. 

It will be noted that with the arm hard over to the right, the 
current which actuates the electro-magnet H is the field current 
and is taken off by the upper one of the contacts at D. Should 
a break occur in the field circuit, this magnet releases the arm 
which is thrown back by the spring. This arrangement is called 
a "no field release." 

These starting-boxes frequently include an overload switch in 
addition to the two releases described above. 



Fig. 312. 

602. Series Motors. — In a series motor, shown diagrammati- 
cally in Fig. 312, the same current passes through both the field 
coils and the armature. As was seen in the discussion of the 



486 ELEMENTS OF ELECTRICITY. 

magnetization curve (Par. 393), at first and when remote from 
saturation, the field H increases nearly in proportion to the ex- 
citing current, hence, at starting, the torque of a series motor, 
IHlx2r, varies practically as the square of the current. These 
motors are therefore especially valuable where great torque is 
needed at starting, for example in trolley cars, hoists, etc. 

603. Speed of Series Motors.— The speed of series motors 
varies inversely with the load and for each particular load there 
is a corresponding speed. This renders them unsuitable for many 
kinds of machines which require a constant speed under varying 
loads, but well adapted for street railways where the speed is of 
necessity constantly varied. 

Consider a generator supplying a series motor M (Fig. 313). 
The power developed by the motor must be equal to that sup- 



wsmvm 



Fig. 313. 

plied by the generator, less the heat loss. This last is small, hence 
the back E. M. F. must be nearly equal to the impressed E. M. F. 
As the back E. M. F. increases, the current through the motor, 
and hence the current through the field coils, grows smaller. The 
field grows correspondingly weaker and to maintain the back 
E. M. F. the speed of the motor must increase. This tendency to 
race under diminished loads is an objectionable feature of a series 
motor. 

604. Change of Direction of Rotation. — It may sometimes be 
desirable to change the direction of rotation of a motor. Suppose 
a, Fig. 314, to represent a shunt motor, the current flowing as 





Fig. 314. 

indicated. The lines of force of the coil will run upwards and the 
rotation will therefore be clockwise. If the direction of the cur- 
rent in the mains be reversed, as shown in b, the lines of force of 



ELECTRO-MECHANICS. 487 

the coil will run downward, but the polarity of the field magnets 
is also reversed, and the rotation will as before be clockwise. 
Hence, reversing the current in the mains does not change the 
direction of rotation. If, however, the direction of the current 
be reversed in either the field or the armature, but not in both, 
the direction of rotation will be changed. 

605. Motor Generators. — Alternating currents are readily 
stepped up or down in voltage by means of a transformer (Par. 
431), but this method is not applicable to direct currents. Where 
such transformation is required, the direct current may be em- 
ployed to operate a motor and this motor in turn operates a gener- 
ator whose armature is so wrapped, or whose field is of such 
strength, as to develop a current of the desired voltage. Instead 
of having the motor rotate the generator by means of a belt or 
gearing, they may both be mounted upon a common shaft. This 
combination is called a motor generator, but electrically it is the 
same as two separate machines. 

A step further may be taken and two sets of coils may be 
wrapped upon the same armature and rotate in a common field. 
Each set has its own commutator, current being delivered to the 
motor commutator and drawn from the generator commutator. 
Transformation is effected by varying the ratio of the number 
of coils or of the number of turns in the two sets of wrappings. 
This machine is called a dynamotor. 



488 ELEMENTS OF ELECTRICITY, 



CHAPTER 43. 

ALTERNATING CURRENTS. 

606. Alternating E. M. F. and Current. — We have seen (Par. 
552), that if a coil rotates at a uniform rate in a uniform field it 
will generate an E. M. F. which varies as the sine of the angle 
through which the coil has turned from its primary position at 
right angles to the field. If the coil is a closed circuit, or forms a 
part of such a circuit, there will be produced in it a current which 
will vary in the same manner. At every revolution of the coil, 
therefore, the E. M. F. and current pass through a complete cycle 
of values, positive and negative. The term alternating is applied 
to an E. M. F., or to a current, which thus undergoes these periodic 
reversals. 

607. Why Considered Separately. — The mere fact that a cur- 
rent reverses its direction at regular intervals might not of itself 
warrant special discussion. There are, however, two properties, 
induction and capacity, which are common to all electric circuits 
and whose effects are conspicuously revealed in varying currents. 
Alternating currents vary continually and with such currents the 
above factors give rise to certain peculiar phenomena, some of 
which appear to contradict the principles which have been developed 
in the preceding pages. Among such we may mention 

(a) The current through a circuit is not always equal to the 
E. M. F. divided by the resistance. 

(b) The sum of the partial drops between two points is not 
always the same as the total drop. 

(c) The sum of the currents in the branches of a divided circuit 
is not always equal to the total current. 

(d) Finally, there may be a flow of current in a broken circuit. 
In the following pages it will be shown that these contradictions 

are only apparent and that Ohm's law is as true of alternating 
currents as it is of direct. In order, however, to be able to explain 
these peculiarities, the subject of alternating currents must be 
considered in detail. We shall therefore begin with certain pre- 
liminary definitions and principles. 



ELECTRO-MECHANICS. 489 

608. Cycle, Period and Frequency. — In Par. 555 it was shown 
that an alternating E. M. F. and current can be represented 
graphically by a sine curve (Fig. 315), the ordinates corresponding 
to the instantaneous values (values at any instant) of the E. M. F. 
or current and the abscissae to the angle through which the coil 




Fig. 315. 

has rotated, or, if the scale of time be used, to the time elapsed 
since the coil moved from its primary position in the neutral 
plane. 

If E m be the maximum instantaneous value of the E. M. F. and 
if the abscissae represent the angle through which the coil has 
rotated, the equation of the E. M. F. curve is 

E = E m . sin e 

If the abscissae represent elapsed time, the equation is 

E = Em . sin wt 

in which co is the angular 
velocity of the coil and t is the time in seconds since the coil lay 
in the neutral plane. 

With every revolution of the coil, the portion of the curve be- 
tween A and B (Fig. 315) is repeated, and the complete set of 
values, positive and negative, between A and B is therefore called 
a cycle. The more rapid the motion of the coil, the greater the 
number of cycles in a given time. The length of time of one cycle 
is called a period and the number of cycles per second is the 
frequency. The word "revolution," as used above, must be inter- 
preted in an electric sense. Thus, in a four pole generator one 
revolution of the armature corresponds to two electric revolutions. 

An additional term, sometimes encountered in books treating 
of this subject, is alternation, an alternation being a reversal of 
direction of E. M. F. or current. There are therefore two alter- 
nations per cycle. The number of alternations is usually given as 
so many per minute. 



490 



ELEMENTS OF ELECTRICITY. 



609. Phase. — For purposes of descriptive location, a cycle is 
considered to be divided into 360 degrees. Any point of the cycle 
is designated as a certain phase, as, for example, the thirty degree 
phase, etc. 

Fig. 316 represents diagrammatically a ring- wound, bipolar, 
alternating current generator. Consider in either half of the 




Fig. 316. 
armature any two adjacent coils, as, for example, B and C. In 
each an E. M. F. is being induced and since in every complete 
revolution of the armature each coil travels around the same path 
and returns to its starting point, the cycle, the period and the 
frequency must be the same for each. At the instant shown how- 
ever, the E. M. F. being induced in C is proportional to the sine 




Fig. 317. 
of the angle CO A, while that being induced in B is proportional to 
the sine of BOA, and will not reach the value of that now in C 
until sufficient time has elapsed for B to move through the angle 
<f>= BOC. The E. M. F. in C therefore has reached a value which 



ELECTRO-MECHANICS. 491 

will not be reached by that in B for a time corresponding to the 
angle 0. This is shown graphically in Fig. 317. The sine curve 
CCCCC represents the E. M. F. of the coil C; the sine curve 
BBBBB represents the E. M. F. of the coil B. 

Two sine curves whose periods are the same and which reach 
their maximum and minimum values simultaneously (see Fig. 265) 
are said to be in phase, otherwise they are said to differ in phase. 
The phase difference may be expressed in time but more frequently 
in angular measure. Thus, the curves in Fig. 317 differ in phase 
by the angle 4> which is represented by the horizontal distance 
CB. If the phase difference is 90°, the curves are said to be in 
quadrature; if it be 180°, they are in opposition. 

It will be shown shortly that an alternating current generally 
differs in phase from its corresponding E. M. F. If the current 
reaches a maximum value after the E. M. F. has passed through 
its maximum, the current is said to lag; on the other hand, if it 
reaches its maximum in advance of the E. M. F., it is said to lead. 
In these cases, the corresponding phase difference is spoken of as 
the angle of lag or as the angle of lead. 

610. Vector Diagrams. — Let the vector OA (Fig. 318), whose 
length represents the maximum value 
Em of an alternating E. M. F. (or cur- 
rent), rotate about the point in a 
counter-clockwise direction and at the 
same uniform angular velocity to as 
the armature. The instantaneous value 
of the E. M. F. (or current) is repre- Fl §- 318> 
sented by the line A B, for AB =E m . sin wt. But DO, the pro- 
jection of OA upon the vertical axis, is equal to AB, hence, when 
the vector makes the phase angle with the horizontal axis, the 
corresponding instantaneous value of the E. M. F. (or current) 
is represented by the projection of the vector upon the vertical 
axis. 

611. Composition of Alternating E. M. F.s. — During the rota- 
tion of the armature of the generator shown in Fig. 316, the coils 
in series combine in producing a resultant E. M. F. Thus, in Fig. 
317 the broken and dotted curve is the resultant E. M. F. curve 
obtained by adding the ordinates representing the corresponding- 
simultaneous values of the E. M. F. in the separate coils. By an 



492 ELEMENTS OF ELECTRICITY. 

application of trigonometry, it can be shown that this resultant 
curve is also a sine curve and is of the same periodicity as the 
component curves, although differing from them in phase. The 
trigonometric process is somewhat tedious and it is thought that 

the following explanation will be 

^'/'/ more easily followed. In Fig. 319, 

C +*** /' ' / the vectors OB and OC represent the 

'"/ ,' / maximum values of the E. M. F. in 

/ /' / the coils B and C of Fig. 316, and 

■■■/■■/ ■•— Vb is the angle of phase difference. The 

'fc^s^ instantaneous value of the E. M. F. 

. JL. in B is, from the preceding para- 
Fig. 319. graph, OB'; the instantaneous value 
of the E. M. F. in C is OC, and the resultant E. M. F. is the sum 
of OB' and OC. Complete the parallelogram CDBO and project 
its diagonal OD upon the vertical axis. CD' is equal to OB', 
hence OD' is equal to the sum of OB' and OC, or is the desired 
resultant. Therefore, the resultant E. M. F. of the coils B and C 
is always given by the projection upon the vertical axis of the 
vector OD, the diagonal of a parallelogram of which the adjacent 
sides represent the maximum values of the E. M. F. in the corre- 
sponding coils and the included angle represents the difference in 
phase. The length of OD represents the maximum value of the 
resultant E. M. F. Since <£, the difference in phase, is constant, 
the vector OD does not vary in length or in position relative to 
OB and OC. Its projections are therefore the ordinates of a sine 
curve of the same periodicity as the E. M. F. curves of the separate 
coils. 

From the foregoing we see that alternating E. M. F.s which 
differ in phase are not compounded by simple addition but in a 
similar manner to that employed in the parallelogram of forces in 
mechanics. 

612. Value of an Alternating Current. — During each cycle, an 
alternating current passes through the entire range of values from 
zero to the positive maximum, thence through zero to the mini- 
mum (negative maximum), thence back to zero. Which of all 
these values should be taken as a measure of the current? The 
logical agreement is reached that such a current is equal to that 
direct current which performs the same amount of work in the 
same length of time. Of the three classes of work which a current 



ELECTRO-MAGNETICS. 



493 



may perform (Par. 444), only one, the heating effect, is inde- 
pendent of the direction of the current, and this is accordingly 
selected as the basis of comparison. 




Fig. 320. 

Let the curve A B (Fig. 320) represent an alternating current 
produced by a coil rotating with an angular velocity co. If the 
maximum value of the current be Im, the equation of this curve is 

i" = I m . sin ut (I) 

Consider any ordinate of this curve as I. The instantaneous 
value of the power being developed at this point is PR (Par. 494), 
R being the resistance of the circuit through which the current is 
flowing. Let M N represent a minute interval of time dt. Since 
work = power X time, the work done by I during this interval is 

dw = PR . dt 

Substituting in this the value of / from (I) 

dw = i l m R . sin 2 oo£ . dt 

The integral of this between the proper limits will give the total 
work performed by the current during the cycle. 



w 



= I 2 m RJ$m\<d . dt 

fsnrW. (co dt) 



ImR 



I m R 



( — % cos cot . sin cot + .V at) + a constant 



Taking this between the limits cot = and cot 



w = I" m R . 



(ii) 



494 ELEMENTS OF ELECTRICITY. 

The work performed by a direct current flowing through the 
same resistance for the same length of time is 

w = PRt 
Since <A = 2ir, t, the time of one cycle = — 

CO 



Substituting, we have 



w=PR. 2 - (Ill) 



Equating the second members of (II) and (III) 

CO CO 

Hence 1=^ = 0.707 Im 

V2 

that is, the alternating current is 
equivalent to a direct current whose value is only .707 of the maxi- 
mum value of the alternating current. This may be otherwise 
expressed by saying that the effective or virtual value of the alter- 
nating current is only .707 of its maximum value. The same 
relation exists between the effective and the maximum voltage of 
an alternating current, and ammeters and voltmeters for use with 
such currents are graduated to read the virtual amperes and volts 
respectively. 

613. Second Deduction. — The foregoing deduction may be 
made without the use of the calculus, as follows: 

B - Let AA and BB (Fig. 321) be two 

y^" x ^X^ co ^ s a ^ right angles to each other, both 

\ rotating at a uniform rate in a uniform 

/ \ \ field and each sending current through a 

/ V ^„~'-'~ \ resistance #. In one complete revolution 

i ""'"T" \~ the work done by the currents from both 

fft'' \ I is twice the work done by the current 

\ \ /' from one. The current from A being 

x \ \ y' I m sin 6, that from B is I m cos 0. The 

~~~~~~ B power developed at any instant by the 

current from A is /^sin 2 0i2; that de- 
veloped at the same instant by the current from B is I m cos 2 R. 
The total instantaneous power is the sum of these two, or 

I 2 m (sin 2 e + cos 2 0) R = I 2 m R 



ELECTRO-MECHANICS. 495 

The total work done during the time t of one complete revolu- 
tion is I 2 m Rt, hence the work done in this time by the current from 
one coil is ^ I 2 m Rt. A direct current i" flowing for a time t through 
the resistance R does work I 2 Rt. 

P Rt = | I 2 m Rt 
Hence j 

I = -7^ as before. 

V2 

614. Self-induction. — Self-induction was explained in detail 
in Pars. 432-436 and it was shown that its characteristic effect is 
to oppose any change in a current-produced field and that it does 
this by setting up a counter E. M. F. which opposes any change in 
the current in the circuit involved. Since alternating currents are 
always changing, it is in dealing with such currents that the con- 
sideration of induction assumes the greatest importance. 




a 

Fig. 322. • 

If an alternating E. M. F. be applied to a circuit of a simple loop 
of wire (Fig. 322 a), the effect of induction may be so slight as to 
be negligible and the current may be considered to follow Ohm's 
law. 

If the same piece of wire be wrapped into a coil of 100 turns and 
the E. M. F. be applied so as to produce the same number of lines 
of force in the field in the same time as before, these are now cut 
one hundred times instead of once and the effect of induction is 
one hundred times as great. . 

Finally, if there be inserted in this coil a soft iron core (Fig. 
322 b) and the E. M. F. be applied, the same change of current 
will produce about 2000 times as many lines of force (Par. 394) 
and the effect of induction will be 200,000 times as great as in the 
first case. These examples show that self-induction is developed 
by the cutting of the lines of force in the embraced field rather 
than by changes in the current in the embracing circuit. 

615. Inductance. — Self-induction is measured by the cutting 
of lines of force produced when the current in the circuit is varied 
one unit. The practical unit, the henry, is the self-induction of 



496 ELEMENTS OF ELECTRICITY. 

that circuit in which a change of one ampere produces a cutting of 
10 8 lines of force. When the self-induction of a circuit is expressed 
numerically, as so many henrys, it is called inductance. The in- 
ductance of a given circuit is constant provided the circuit is 
distant from magnetic bodies. If it be not distant from such 
bodies, owing to their saturation, the field does not vary uniformly 
with the current. 

Although the inductance is thus constant, the counter E. M. F. 
which it is instrumental in producing, and whose effect is so im- 
portant, is not at all constant but varies with the rate of change 
of the current (Par. 432) and has therefore a different value at 
every different phase and for every different frequency employed. 
This will be shown more clearly later on. 

616. Inductance and Resistance. — Inductance and resistance 
agree in that they oppose the flow of current in a circuit, but here 
the similarity ends. The following will bring out the difference 
between the two. 

(a) The resistance of a circuit is constant and does not vary 
with changes in the current. The inductance of a circuit appears 
only when the current is changing and the counter E. M. F. which 
it sets up is proportional to the rate of this change. 

(b) Resistance does not vary with the geometric form of the 
circuit nor with the proximity of magnetic bodies. Inductance 
depends essentially upon these factors. 

(c) The energy spent in overcoming resistance is lost in the 
form of heat. That spent in overcoming the induction counter 
E. M. F. (Par. 359) is periodically absorbed in the field about the 
conductor as the current rises and is restored to the circuit as the 
current falls. As an analogy, the energy spent upon a fly-wheel 
does two things: (1) it overcomes the friction of the bearings and 
is thus lost as heat, and (2) it is absorbed by the wheel which, 
after the power is shut off, continues to turn and thus restores 
the absorbed energy. 

All circuits contain resistance, inductance and capacity, but 
one or more may be so small as to be negligible. For the sake of 
simplicity we shall first consider a circuit in which the capacity 
may be disregarded. 

617. Alternating E. M. F. in a Circuit Having Resistance and 
Inductance. — The instantaneous value of the current produced 



ELECTRO-MECHANICS. 497 

in a coil rotating at a uniform rate in a uniform field is (Par. 612; 

/ = Im . sin cot 

In this expression, co is the angular velocity of the moving coil, 
whence cot is the angular distance through which the coil rotates 
in t seconds. In one revolution the coil turns through the angle 
2ir. If the frequency be /, that is, if the coil makes / revolutions 
per second, the angular distance through which it travels in one 
second is 2irf and in t seconds is 2tJL We may therefore sub- 
stitute 2irjt for cot in the above expression, whence 

I = Im . sin 2irft 

If the resistance of the circuit be R, the E. M. F. required to 
drive the current I through this resistance is, from Ohm's law, 
Er = IR, or, substituting the above value of I 

E B = R(I m . sin 27r#) 

This E. M. F., which is variously called the active, the efficient, 
or the power E. M. F., reaches its maximum value I? n R when 
sin 2wft=l, that is, at the 90° and the 270° phases, or at B and D 
(Fig. 323), and may be represented by the sine curve AFCGE, 
the corresponding current being in phase with it and being repre- 
sented by the sine curve ASCTE. 

Should there be in the circuit an inductance of L henry, there 
will be produced a counter E. M. F. whose value is (Par. 434) 

I = Im . sin 2irft 
~-rr = Im . 2tt/ . COS 2irft 

whence 

E B =-L.I m .2Trf.cos2Tft 

This counter E. M. F. may therefore be represented by a sine 
curve. It reaches its maximum value I m . 2irfL when cos 2-rrft = 1, 
that is, at the 0° and the 180° phases, or at A, C and E (Fig. 323). 
It is therefore in quadrature with the E. M. F. represented by 
the curve AFCGE. Also, since this E. M. F. opposes any change 
in the existing current, it is positive as the latter falls and negative 
as the latter rises. It is a maximum when the current passes 



Since from above 



498 



ELEMENTS OF ELECTRICITY 



through zero, since at this moment the rate of change of the cur- 
rent is greatest, and it is zero when the current is a maximum, 
either positive or negative. It may therefore be represented by 
the sine curve HBJD K. 
p 




Fig. 323. 

In order to drive the current I through the circuit, the im- 
pressed E. M. F. must be greater than that required by Ohm's 
law of a direct current, for it must not only be sufficient to over- 
come the ohmic resistance but also to counterbalance the back 
E. M. F. due to self-induction. 

The curve LBMDN represents the E. M. F. required to over- 
come the counter E. M. F. Its prdinates are equal but of opposite 
sign to the corresponding ordinates of the curve HBJDK. The 
impressed E. M. F. is the resultant obtained by compounding 
the E. M. F. represented by the curve AFCGE and that repre- 
sented by the curve LBMDN. The curve LPFMQGN, obtained 
by adding the corresponding ordinates of these two curves, 
represents this resultant. It will be noted that it reaches its 
maximum at P before the current reaches its maximum at S, 
that is, it leads the current by a difference of phase correspond- 
ing to RB. In alternating current circuits containing resistance 
and inductance alone, the current always lags behind the im- 
pressed E. M. F. 

618. Graphic Construction of E. M. F. and Current Curves. — 

The power E. M. F., or E. M. F. required to overcome the ohmic 
resistance, and the E. M. F. required to counterbalance the 
E. M. F. of self-induction, may be compounded as just explained. 
They may also be compounded according to the method described 
in Par. 611. Thus, to find the instantaneous values of the various 



ELECTRO-MECHANICS. 



499 



E. M. F.s and current at any phase, such as x, Fig. 324. Lay of! 
oa to represent the maximum value, I m R, of the power E. M. F. 
and making with the horizontal axis an angle 6 corresponding to 
the phase angle Ex. On this same line, since the current is in 
phase with this E. M. F., lay off oc to represent the maximum 
value Im of the current. Lay off ob at right angles to oa (the 
two E. M. F.s being in quadrature) and of a length to represent 
the maximum value, ImZirfL, of the E. M. F. to overcome the 
E. M. F. of self-induction. The diagonal od of the parallelogram 
constructed upon oa and ob is the vector corresponding to the 
required impressed E. M. F. The projection of oa upon the 




Fig. 324. 



ordinate at x locates the point A of the curve of power E. M. F., 
that of ob locates the point B of the curve of E. M. F. to counter- 
balance the induced E. M. F., and that of od locates the point D 
of the curve of impressed E. M. F. Finally, the projection of oc 
upon the ordinate at x locates the point C of the current curve. 

619. Inductive Reactance. — The counter E. M. F. due to self- 
induction varies with the rate at which the lines of force are cut. 
It therefore varies not only with the inductance, or number cut 
when the current is varied one ampere, but also with the rapidity 
with which the current changes. In alternating currents this is 
a function of the number of cycles per second, that is, of the 
frequency. In Par. 617 it was shown that this E. M. F., which 
is also called the reactive E. M. F., is in quadrature with the power 
E. M. F. and that its maximum value is 



Eb — Ini.2irfL 



500 



ELEMENTS OF ELECTRICITY. 



The factor, 2wfL, is called the inductive reactance. It obviously 
varies with the frequency / and with the inductance L. It is 
measured in ohms, as might be inferred from the fact that when 
multiplied by current the product is E. M. F. By expressing 
it in its dimensional formula, it may be shown to be of the same 
dimensions (a velocity) as resistance (Par. 547). It is sometimes 
denned as that factor by which the maximum value of an alternat- 
ing current in a circuit containing inductance is multiplied in 
order to obtain the maximum value of the reactive E. M. F. The 
reactance of a circuit for a given frequency is obtained in ohms 
by multiplying the inductance in henrys by 2w times the frequency. 

620. Impedance. — Examination of Fig. 324 will show that od, 
the maximum value of the impressed E. M. F., is the hypothe- 
nuse of a right-angled triangle whose sides are oa = I m R, the 
maximum value of the power E. M. F., and ad = ob = I m .2irfL, 
the maximum value of the reactive E. M. F. It follows that 
(Fig. 325 a) 

whence 

Im 



E' m = (imRy + (Im.2rfLy 

htm 



VRz + (27T/L) 2 

The resemblance of this expression to Ohm's law is obvious. 
The denominator of the fraction in the second member is meas- 
ured in ohms since it is composed of the resistance and the re- 




Fig. 325. 

actance, both of which are measured in ohms. It is called the 
impedance since it represents the combined effect of the ohmic 
resistance and the reactance in impeding the flow of the current. 
It is sometimes defined as that factor by which the current in an 
alternating circuit is multiplied in order to get the corresponding 
impressed E. M. F. It will be noted that if /=0, the current 
becomes direct and the expression reduces to Ohm's law. 



ELECTRO-MECHANICS. 501 

Inspection of the expression will show that the impedance is 
itself the hypothenuse of a right-angled triangle whose sides 
are the resistance and the reactance (Fig. 325 b). 

It is also seen that the angle of lag, doc (Fig. 324), is given by 
the relation 

_da _ 2irfL _ reactance 
oa R resistance 

and also by the relation 

_ oa _ Er_ _ power E. M. F. 
^ ~ od ~ Em ~ impressed E. M. F. 

or, the cosine of the angle of 
lag is equal to the ratio of the power E. M. F. to the impressed 
E. M. F. This may be otherwise expressed by saying that if the 
impressed E. M. F. be multiplied by the cosine of the angle of lag, 
the result is the E. M. F. required to overcome the ohmic resist- 
ance, i. e., the power E. M. F. 

621. Choke Coils.— The maximum value of an alternating 
current in a circuit containing resistance and inductance is shown 
in the preceding paragraph to be 

j _ Em 

VR* + (27T/L)* 

If R, the resistance of the circuit, be small, its value may be 
negligible as compared to that of 2irfL, the reactance, and there- 
fore the current may depend more upon the reactance of the cir- 
cuit than upon its resistance. 

The reactance varies directly with the inductance and the 
frequency. The inductance varies with the geometric arrange- 
ment of the circuit and the proximity of magnetic bodies. The 
frequency in currents for commercial purposes ranges from 25 to 
130. If the current is to be employed for electric lighting, the 
frequency should not fall below 50, otherwise there will be a per- 
ceptible vibration or nicker in the lamps. 

It is possible to place in an alternating current circuit a coil of 
large wire, and hence a small resistance, with a soft iron core 
whose position may be varied at will. As the core is inserted in 
the coil, the reactance is increased and the current through the 
coil is cut down; as the core is withdrawn, the reactance is de- 
creased and a greater current passes through. 



502 ELEMENTS OF ELECTRICITY. 

Such an arrangement is called a reactance coil or a choke coil 
and is frequently used for such purposes as regulating the bril- 
liancy of the lights in a theatre, or for controlling the current 
applied through a starting box to an alternating current motor. 
It possesses the great advantage over rheostat control in that it 
diminishes a current by setting up an opposing E. M. F. and hence 
without loss of energy, while, in the case of the rheostat, power 
is reduced by frittering away a portion in heat which waste must 
be paid for by the consumer. 

622. Explanation of Operation of Choke Coil. — If a more physi- 
cal conception of the operation of a choke coil be desired, it may 
perhaps be obtained from the following. In Par. 436 it was shown 
how induction retards the growth of a current. It could have been 
shown in a similar manner that inductance also retards the decay 
of a current, a dying current being represented by a logarithmic 
curve also whose ordinates are complementary to those of the 
curve representing the growing current. Fig. 207 shows that under 
the conditions given, the current in the circuit whose inductance 
was one henry required, after the E. M. F. was impressed, about 
one second to reach the value of six amperes. Suppose this to 
have been an alternating current of a frequency of 50. In one- two- 
hundredth of a second after the current started to rise, or when it 
had reached a value of about .03 ampere, the E. M. F. would be 
reversed and the current would be beaten back. It would die 
down as slowly as it rose and would then start to rise in the op- 
posite direction but in one-hundredth of a second after it had been 
beaten down it would encounter a reversed E. M. F. and would 
be checked and driven back, and so on, or, figuratively, it would 
be a shuttle cock at the mercy of the alternating E. M. F.s. We 
thus see that inductance makes the changes in the current slug- 
gish and that increase of frequency causes the rising current to 
be driven back more promptly. 

623. Inductance and Resistance in Series. — The fact that in 
alternating current circuits containing inductance and resistance 
alone the current always lags behind the impressed E. M. F. (Par. 
617) affords an explanation of some of the peculiarities of alternat- 
ing currents to which reference was made in Par. 607. As an 
illustration, Fig. 326 represents a switch A by which an alternat- 
ing E. M. F. may be thrown upon a circuit including in series a 



ELECTRO-MECHANICS. 



503 



coil BC with an iron core, and therefore of considerable inductance, 
and a rheostat whose resistance is assumed to be non-inductive, 
or purely ohmic. Suppose the switch to be closed and that with 
a voltmeter we read first the drop across the inductance BC, then 
the drop across the resistance DE, and finally the total drop 
between B and E. This total drop will be found to be less than 
the sum of the partial drops. The explanation is that the volt- 
meter takes no account of phase but indicates the virtual volts 



— 3 




VOLTMETER 



RHEOSTAT 



Fig. 326. 



between its terminals as if the E. M. F. remained constantly at 
this value. The current through the circuit at any one instant 
is of course the same at every point, but while it is in phase with 
the E. M. F. across DE, it lags 90° behind the E. M. F. across BC. 
The maximum E. M. F. across BC occurs therefore one-quarter 
of a period in advance of the maximum E. M. F. across DE. The 
total drop is therefore not the sum of the partial drops, since the 
maximum values of these do not occur simultaneously, but is 
represented by the hypothenuse of a right triangle whose remain- 
ing sides are the partial drops. 

624. Inductance and Resistance in Parallel. — Fig. 327 repre- 
sents an inductive resistance BC and a non-inductive resistance 




Fig. 327. 

DE connected in parallel in an alternating current circuit. A, F 
and G are ammeters arranged to read the currents in the main 




504 ELEMENTS OF ELECTRICITY. 

circuit and in the branches of the divided circuit respectively. 
It will be found that the sum of the currents indicated by F and G 
is greater than the current indicated by A. This happens because, 
as explained in the preceding paragraph, the ammeters take no 
heed of phase but indicate the virtual values of the separate cur- 
rents as if these currents were constant, or as if their maxima 
occurred simultaneously. The drop over the two branches is 
always the same, being the difference of potential between M and 
N, but the current through DE is in phase with this E. M. F. 
while the current through BC lags 90°. When the current through 
DE is a maximum, the current through BC is still one-quarter 
period removed from its maximum and is correctly the difference 
between the current through A and that through G. The am- 
meter F, however, indicates the virtual value of the current 
through BC, as if the current were constantly of this strength. 
The currents through F and G are in quadrature and therefore 
the total current is represented by the hypothenuse of a right 
triangle whose remaining sides are the currents as indicated by 
F and G. 

From the foregoing we see that the current through resistance 
and reactance in series is the same at every point, but the voltage 
across the combination is the vectorial resultant of the separate 
drops as given by a voltmeter. On the other hand, the voltage 
across resistance and reactance in parallel is the same over each, 
but the total current is the vectorial resultant of the separate 
currents as given by an ammeter. 

625. Capacity. — The subject of capacity was discussed in 
Chapter 10 and it was there shown that the capacity of a con- 
denser is not measured by the quantity of electricity which it 
can contain but by the quantity which must be imparted to it 
in order to raise its potential unity. 

If two points between which there exists a difference of poten- 
tial be connected by a conductor, there will be produced a current 
which will vary directly with this difference of potential and which 
will continue to flow so long as a difference exists. If, therefore, 
a source of E. M. F. be connected to the terminal of a condenser, 
a current will flow into the condenser so long as the potential of 
the source is higher than that of the condenser. This current, 
however, will not be of constant strength, for as the condenser 
becomes charged its potential rises, hence the difference of poten- 



ELECTRO-MECHANICS. 



505 



tial between it and the source grows smaller, and it is to this 
difference of potential that the current is proportional. We may 
regard the potential of the condenser as a counter E. M. F. which 
opposes the charging E. M. F. and thereby diminishes the current. 




Fig. 328. 

As an analogy, Fig. 328 represents a large tank A of water of 
unvarying head connected through a pipe closed by a stop cock 
to the smaller tank B. The difference of the level of the water in 
A and B determines whether there shall be a flow when the stop 
cock is opened. If at first B be empty, the flow is urged by the 
full head of water in A and the current is a maximum. When, 
however, B has been partly filled, as shown in the figure, its head 
is opposed to that of the water in A and the flow is determined 
by the diminishing difference in level e; therefore, as B fills up, 
the current dwindles to zero. 

626. A Condenser in an Alternating Current Circuit. — Suppose 
a condenser to be connected in series in an alternating current 
circuit, as shown in Fig. 329. So long as the potential of the brush 




Fig. 329. 

A is higher than that of the terminal B, a current will flow into 
the condenser, and when the potential of A is a maximum, the 
condenser will contain a charge Q, the maximum under the given 
conditions. As the potential of A diminishes, Q flows out and 
B is entirely discharged when the potential of A is zero. As the 



506 



ELEMENTS OF ELECTRICITY. 



potential of A continues to sink to a negative maximum, a charge 
Q flows into the coating D of the condenser and finally flows out 
again as the potential of A returns to zero. It is thus seen that 
although the circuit is broken at the condenser, a charge Q flows 
through the circuit four times in each cycle. If the capacity of 
the condenser and the frequency be sufficiently great, an incan- 
descent lamp, connected as shown, may be made to glow by this 
oscillating charge. 

627. E. M. F. and Current Curves in Case of Capacity. — The 

foregoing may be shown graphically as follows. The sine curve 
EMFGH, Fig. 330, represents the impressed E. M. F., or the 
potential of the brush A. The current from A to the condenser 
B is determined by the difference of potential between A and B 
and is a maximum when the potential A is increasing most rapidly. 
This maximum rate of increase occurs at M when the potential 
of A is zero. It is here that the tangent to the curve is steepest 
or the curve climbs up most rapidly. The current therefore, 
represented by the curve JKLNO, reaches a maximum value 
M K at this point. When the potential of A reaches its maximum 
at L, the condenser is fully charged and the current no longer 
flows into it. At this point the current curve is at zero. As 




the potential of A falls, the condenser discharges, or the cur- 
rent is now negative. As before, the negative current is a maxi- 
mum when the potential of A is falling most rapidly, and this is 
the case at G where the potential of A is again zero. Finally, 
the current is again zero at where the potential of A is a negative 
maximum. It is thus seen that in the case of capacity, the cur- 
rent curve leads the E. M. F. curve and is in quadrature with it. 



ELECTRO-MECHANICS. 507 

628. Capacity Reactance. — The instantaneous value of the 
E. M. F. in an alternating current circuit is 

E = Em . sin id 

If this circuit contains capacity alone, the current leads the 
E. M. F. by 90° and is given by 

/ = Im . COS mt 

The instantaneous value of the power developed is (Par. 494) 

IE = ImEm . sin id . cos <d 

The work done in a time dt is 

dw = ImEm . sin cot . cos wt . dt 

Since the condenser is charged in one-fourth of a period (Par. 626) 
if this expression be integrated between the limits t = and 

t = jl—j = ~ (Par. 612), it will give the work expended in 

charging the condenser. 
Performing the integration 

w = — — - • o (sin 2 <d) -+- a constant 

Taking this between the above limits 

ImEm /TX 

w = -£T (I) 

But in Par. 97 it was shown that the work spent in charging a 
condenser of capacity C is 

w=l-E 2 m C (II) 

Equating (I) and (II) and solving for E m 

Em = lm ' —p^ 

Substituting for co its value 2tt/ (Par. 617) 
Em = Im ' r/^i 



508 ELEMENTS OF ELECTRICITY. 

Whence also, since Em = E V V2 and Im = IvV2 (Par. 612) 

Ev = Iv '2rfC 

E v and I v being the virtual 
E. M. F. and current respectively. 

The factor fr , is called the capacity reactance of the circuit. 

Z7T/C 

It is quite analogous to the inductive reactance discussed in Par. 
619. It is measured in ohms and its dimensional formula (Par. 
547) shows it to be of the same dimensions, a velocity, as resist- 
ance. It is that factor by which the maximum value of an alter- 
nating current in a circuit containing capacity must be multiplied 
in order to obtain the value of the reactive E. M. F. due to 
capacity. 

629. Alternating E. M. F. in Circuit Containing Resistance and 
Capacity. — If the circuit contains both resistance and capacity, 
in order to drive a current I m through it, the impressed E. M. F. 
must be sufficient to overcome both the ohmic resistance and the 
capacity reactance. The E. M. F. to overcome the ohmic resist- 
ance is ImR, that to overcome the capacity reactance is Im . £r , > 
and these being in quadrature (Par. 627) 



E 2 m = (ImR) 2 - ( Im . 2~Tq) 



whence T E? 



vW 



2tt/C 

an expression analogous to 
the one deduced in Par. 620, the denominator being the impedance. 
It will be noted that inductive reactance varies directly with 
the frequency /, while capacity reactance varies inversely with 
this factor. Changes in the frequency therefore produce diametri- 
cally opposite results in the reactances. As the frequency increases, 
the current through an inductive circuit decreases while that 
through a capacity increases. On the other hand, as the frequency 
decreases, the current through an inductive circuit increases and 
that through a capacity decreases. 



ELECTRO-MECHANICS. 509 

630. Alternating E. M. F. in Circuit Containing Resistance, 
Inductance and Capacity. — In the most general case, in order to 
drive a current Im through an alternating current circuit contain- 
ing resistance, inductance and capacity, the impressed E. M. F. 
must be sufficient to overcome the ohmic resistance and the com- 
bined reactance of the inductance and capacity. It has been shown 
(Par. 617) that in the case of inductance the current lags 90° ; on 
the other hand, in the case of capacity (Par. 627) the current 
leads by 90°. The E. M. F.s to overcome these separate react- 
ances therefore differ in phase by 180° and are combined by simple 
subtraction, hence the resultant reactance is 



2tt/L 



1 



pression for the current is 

Im = 



2tt/C 

and the most general ex- 

Em 



631. Electric Resonance. — Fig. 331 represents an alternating 
current circuit in which there are connected in series a coil of 
resistance R and inductance L and a condenser of capacity C. 




A » 



Fig. 331. 




From the preceding paragraph, the current through the combina- 
tion is 

i- E 

Vv + fa-Wc) 

If in this expression we assign a regular series of values to /, the 
frequency, the remaining factors being kept constant, and plot 
the corresponding values of the current, it will be seen that at a 
certain value of /, which may be called the critical frequency, the 



510 



ELEMENTS OF ELECTRICITY. 



current jumps abruptly to a maximum. Inspection will show 
that this maximum is reached when 2tt/L = ,„ , in which case 

Z7T/C 

the above expression reduces to Ohm's law. In this case also 
/ = ~ — 7=, and the periodic time= 1//= 2WLC seconds. The 

Ztt V L/C 

above is shown in Fig. 332, the curve representing the values for 




40 SO 60 
FREQUENCY 

Fig. 332. 



90 JOO 



different frequencies of the current in a circuit in which £'=110 
volts, R = 2 ohms, L = 0.5 henry and C = 25 microfarads. At a 
frequency of about 45, the current mounts suddenly to 55 amperes, 
while at a frequency of 5 more or 5 less it is but little greater than 
three amperes. 

If a heavy pendulum be given a series of slight impulses, no 
especial effect will be produced unless these impulses be timed 
at the natural period of vibration of the pendulum, in which case 
their effect is cumulative and it may be made to swing through a 
wide arc. 

Again, if various tuning forks be caused to vibrate near the open 
end of a closed organ pipe, no effect will be produced until a fork 
is used whose period of vibration corresponds to the natural period 
of vibration of the column of air within the pipe, and when this 
happens the column of air will vibrate in unison with the fork and 
the total volume of sound emitted will be greatly increased. This 
phenomenon is called resonance. 

In the case of the alternating current circuit under considera- 
tion, the E. M. F. is not applied steadily but in a series of impulses 



ELECTRO-MECHANICS. 51 1 

following each other at regular intervals. These impulses produce 
no very marked effect until the critical frequency is reached, at 
which time the current rises abruptly to its maximum value. 
From analogy, the circuit is now said to possess electric resonance. 
Resonance exists in an alternating current circuit whenever 

2irfL= ,_ , or when the inductive reactance is exactly counter- 

AttJC 

balanced by the capacity reactance. 

632. Resonance with Inductance and Capacity in Series. — 

When resonance exists in a circuit containing inductance and 
capacity in series (Fig. 331), the current follows Ohm's law and the 
impressed E. M. F. is simply the IR drop. The fact, however, 
that the inductive and the capacity reactances neutralize each 
other, or that their sum is zero, does not mean that they are 
separately zero. On the contrary, the difference of potential across 
the terminals of the inductance is I.2irfL (Par. 619) and that 

across the terminals of the condenser is / . £ry (Par. 628) and 

these may very greatly exceed the impressed E. M. F. For ex- 
ample, in the numerical example given in the preceding paragraph, 
while the impressed E. M. F. is 110 volts, the drops across the 
terminals of the inductance and of the condenser are each 7778 
volts. 

633. Resonance with Inductance and Capacity in Parallel. — A 

particular case of resonance is where the inductance and capacity 
are in parallel as shown in Fig. 333. The current on arriving at A 




Fig. 333. 

divides, but in the branch L it is retarded while in the branch K 
it is advanced an equal amount. The result is that the loop 
AKBL acts as a short circuit, the current surging around it in 
one direction during one-half of a period and in the other direction 
during the remaining half. Although the current in the main cir- 
cuit may be small, that in this loop may be very large. This cap 
be shown graphically, for the current in the main circuit is the 
resultant of the currents in L and K (Par. 624), that is, it is the 



512 



ELEMENTS OF ELECTRICITY. 



diagonal of a parallelogram whose adjacent sides made with each 
other an angle of very nearly 180°. 

634. Power in an Alternating Current Circuit. — In an alternat- 
ing current circuit the instantaneous value of the power is the 
product of the corresponding simultaneous instantaneous values 
of the E. M. F. and the current (Par. 494). Two cases may arise: 
(a) the E. M. F. and current may be in phase, or, (b) they may 
differ in phase. 

If the E. M. F. and current are in phase, at any one instant 
they are either both positive or both negative and therefore their 
product, the power, is always positive. This is shown in Fig. 334 




Fig. 334. 



in which the broken curve representing the instantaneous values 
of the power lies always above the horizontal axis. The power 
curve is seen to be periodic and of twice the frequency of the 
E. M. F. and current curves. Since its ordinates represent rate 
of doing work and its abscissae represent time (Par. 608), the 
area included between the curve and the horizontal axis represents 
work performed by the current. The work is positive, for whether 
the current flow in or out it performs work in overcoming the 
resistance of the circuit. 

If the E. M. F. and current differ in phase, their simultaneous 
values must at times differ in sign and at these times their product, 
the power, must be negative. The power curve, therefore, as 



ELECTRO-MECHA NWS. 



513 



shown in Fig. 335, extends below the horizontal axis. The areas 
of the loops below this axis represent negative work, or energy 
imparted to the field about the circuit and restored by this field 
to the system (Par. 616). 



/ 1 N 


V \ 


/ 


\ 




k/ 1 


\ \ 


/ 

/ 


\ 




\ 7 / <&^ 


— *\i. 


/ 
/ 
/ 
V / 
\ / 


\ 
\ 

\ / 
\ / 




'/ Is 




>./ 


\/ 




I s v^ 




\<-'' \ 


/ \ 


^y \ 



Fig. 335. 

635. Power Factor. — -In Par. 613 it was shown that the work 
done by an alternating current in one cycle is \ I^Rt, Im being 
the maximum value of the current, R the resistance of the cir- 
cuit and t the time of one cycle. By dividing this by t we get the 
average rate of doing work, in other words, the average power, 
hence 



which may be written 



s I 2 m R watts 



&) 2 - R 



In the same paragraph it was shown that I v , the virtual current, 
is equal to I m /V2, hence 

p = I 2 v R = l v . I V R 

But I V R is that component of the virtual E. M. F. which is in 
phase with the current, hence (Par. 620) 

IvR = E v . cos </> 
hence 

P = IvEv . cos </> watts 

or the average power in 
an alternating current circuit is equal to the product of the virtual 



514 ELEMENTS OF ELECTRICITY. 

current, the virtual E. M. F., and the cosine of the angle of lag (or 
lead). 

The power in an alternating current circuit must be read by a 
wattmeter, for, except when the E. M. F. and current are in phase, 
it can not be determined by taking simultaneous measurements 
with an ammeter and a voltmeter and multiplying these readings 
together. The product of these readings, IvE v , is called the 
apparent power, and cos <£ is called the power factor, since, as shown 
above, it is that factor by which the apparent power must be 
multiplied in order to obtain the true power. 

If <f> becomes 90°, that is, if there is no resistance in the circuit 
so that the E. M. F. and current are in quadrature, cos = and 
the power as given above reduces to zero. In this case, the area 
of the negative loops of the power curve (Fig. 335) equals that of 
the positive loops. 



ELECTRO-MECHANICS. 515 



CHAPTER 44. 

ALTERNATING CURRENT GENERATORS. 

636. Alternators. — The fundamental principles of alternating 
current generators have already been brought out in the chapter 
treating of direct current generators. It was there shown that 
the currents generated in the revolving armatures described were 
all alternating and to rectify them an especial contrivance, the 
commutator, was required. It would therefore seem that should 
the commutator be discarded and collector rings (Par. 553) be 
substituted in its place, we would obtain an alternating current 
generator, or, as it is more briefly named, an alternator. However, 
we also saw that in the D. C. generators the fields were self- 
excited, the direct current for this purpose being drawn from the 
commutator. The discarding of the commutator therefore in- 
volves a change in the methods of exciting the field coils, and for 
this and for other reasons it is necessary to consider these machines 
a little more in detail. 

637. Field Excitation of Alternators. — In most alternators the 
field coils are excited by a current drawn from a separate source, 
such as from a battery or from a small D. C. generator. This 
auxiliary generator, the exciter, may be operated in a number of 
ways, (a) It may be entirely independent, (b) It may be driven 
by a belt from a pulley on the shaft of the alternator, (c) It may 
be mounted upon an extension of this shaft, (d) It may form an 
integral part of the armature of the alternator itself. In this case 
the armature must be provided with both collector rings and 
commutator, the field current being drawn from the latter. 

638. Compound Alternators. — As the current through an alter- 
nator increases, the internal drop also increases and consequently 
the voltage across the brushes diminishes. We have seen (Par. 
511) how important it is in the case of electric lighting (for which 
alternating currents are largely used) that the voltage delivered 
to the lamps should be constant. To secure this constancy of 
potential, the voltage across the brushes must not only not fall 



516 



ELEMENTS OF ELECTRICITY 



with increase of current but must actually rise. In direct current 
generators this is secured by compounding (Par. 588). This 
remedy is not directly applicable to alternators but there are 
several ways in which an approximation to it may be obtained. 
One of these is shown diagrammatically in Fig. 336 which repre- 
sents the armature of an eight-pole alternator. The current 
leaving the armature windings at the coil A, before reaching the 
corresponding collector ring passes through the primary of a step 
down transformer B. The core of this transformer is attached 
to the armature spider or forms a part of it and therefore rotates 




SERIES FIELD COILS 



Fig. 336. 



with the armature. The current from the secondary is taken to 
a commutator CD which is mounted upon the armature shaft 
close to the collector rings but which, for the sake of clearness, is 
represented in the diagram as moved off to the right and turned 
sidewise to the observer. This commutator has only as many 
segments as the alternator has poles, and the alternate segments 
are connected together as shown. Brushes pressing against it 
deliver a rectified current to the series field coils. An increase 
in the current in the external circuit, and hence in the primary of 
the transformer, causes an increase in the current through the 
secondary, and hence through the field coils, which in turn causes 
the desired rise in voltage. 

It is sometimes possible to dispense with the transformer and 
to take the current direct from the coil A to the commutator. 
As a rule, however, alternators generate a high voltage current 
which, besides being dangerous, is apt to cause excessive sparking 



ELECTRO-MECHANICS. 517 

at the commutator. For these reasons the transformer is to be 
preferred. 

639. Alternators Usually Multipolar. — It is in general necessary 
that an alternator should be multipolar. This will be seen from 
the following. A small alternator may be driven at 1800 revolu- 
tions per minute. This speed may be exceeded by some of the 
turbine driven machines but is near the limit for the average 
small generator and much above the limit for large machines. At 
this rate, a point on the circumference of a twelve inch armature 
is travelling faster than a mile per minute. But at 1800 revolu- 
tions per minute the frequency of the current from a bipolar 
machine is only 30. This, we have seen (Par. 621), is too low for 
the operation of an incandescent lamp. Moreover, frequencies 
as high as 120 are often required. Since the speed of the alter- 
nator can not be increased, such frequencies can be obtained 
only by increasing the number of poles. In some of the larger 
modern alternators, the number of poles has approached one 
hundred. 

640. Classes of Alternators. — As shown above, the classifi- 
cation of D. C. generators according to the method of field excita- 
tion into series, shunt and compound machines is not applicable 
to alternators. They may, however, be divided into two general 
classes; (a) those with stationary field and revolving armature, 
and (b) those with stationary armature and revolving field. Of 
this second class there is a subdivision, the inductor alternator, 
in which, although the field revolves, the exciting current passes 
through a single coil which is stationary (Par. 643). From an 
electrical standpoint, there is no call for these divisions, the 
principle being the same in all, but each possesses certain minor 
advantages and it is therefore desirable to consider them separately 
though briefly. 

It will shortly be shown that alternators may be designed to 
deliver a single current or two or more separate and distinct 
currents which differ in phase and accordingly they are also 
classed as single phase or as polyphase. 

641. Alternators with Revolving Armatures. — The simplest 
form of alternator with revolving armature is figured and ex- 
plained in Par. 553. The majority are multipolar. A diagram- 



518 



ELEMENTS OF ELECTRICITY. 



matic end view of such a machine is given in Fig. 337, and in Fig. 
338 a similar four-pole machine is shown as rectified, that is, the 
field, the armature and the collector rings are represented as 
having been straightened out. With clockwise rotation, the coils 




o 



FIELD EWtlNCn 
*/"" / CURRENT 



Fig. 337. 

A, B, C, D move from left to right as indicated by the large 
arrow. Application of the rule given in Par. 421 shows that at 
the instant represented a clockwise E. M. F. is induced in A and 
in C and a counter-clockwise E. M. F. in B and in D, but since 



/ A> 


h* |/ 1 S |/ 1 N 1/ 1*1/ 


> F 




J I F 


L 


V 


6 



Fig. 338. 

these coils alternate in the direction of their winding, they add 
their respective E. M. F.s. The current passes into the external 
circuit from the collector ring EE through the brush G and returns 
through the brush H which is in contact with the ring FF. The 
direction of this current is reversed as A passes beneath the center 
of S. 



ELECTRO-MECHANICS. 



519 



642. Alternators with Revolving Field. — In alternators with 
revolving field, the field may retain its relative position exterior 
to the armature, but far more frequently they interchange places 
and the revolving field is internal. Roughly speaking, the field 
core resembles the hub of a wheel whose spokes have all been 
sawed off to a length of two or three inches. The field coils are 
wrapped about these spokes, alternating in direction so as to 
obtain the desired polarity. The exciting current is brought in 
and taken out by means of a pair of slip rings (identical in opera- 
tion with collector rings). Fig. 337 would represent such a ma- 
chine if the field circuit and the external circuit were interchanged, 




Fig. 339. 

that is, if the exciting direct current were brought in through the 
collector rings and if the present field circuit were used as the 
external circuit. The armature, Fig. 339, is built up of laminated 
punchings, spaces being left for ventilation. The coils are placed 
in slots and held in position by wedges. 

The great advantage of this form of alternator is that the cur- 
rent, which we have seen is usually of high voltage, is taken off 
through fixed connections, which may be insulated to any desired 
degree, and only the relatively small exciting current passes 
through the sliding contacts on the slip rings. 



520 



ELEMENTS OF ELECTRICITY. 



'—*•'--> 1 




r i 





Fig. 340. 



643. The Inductor Alternator. — The inductor alternator, shown 
diagrammatically in section in Fig. 340, possesses the advantage 

of having no sliding contacts and therefore requires 
no collecting rings or brushes and is free from the 
sparking which occurs in other machines. It con- 
sists of an inductor, a rotating toothed soft-iron disc 
around whose edge there is a deep groove. In this 
groove lies the annular field coil C which is fastened 
to the frame work and therefore does not rotate 
with the inductor. When a current flows through 
C, the inductor becomes magnetized, its faces 
being of opposite polarity and hence the teeth on 
one side being all of like polarity. The frame 
work which surrounds this revolving inductor 
has inward projections corresponding to the mov- 
ing poles, and upon these projections the armature 
coils are wrapped. Since the poles on each side do not alternate 
in polarity, there is no reversal of flux through the armature coils 
but this flux rises and falls and thus produces an alternating cur- 
rent in the coils. 

644. Polyphase Alternators. — Suppose that the ends of the two 
coils in Fig. 269, instead of terminating in the commutator seg- 
ments as shown, should each be connected to a separate collector 
ring as shown in Fig. 341. There being no electrical connection 
between these coils, a pair of brushes C could be applied to the 
rings of the coil B and lead current from this coil into an external 
circuit. A second pair of brushes D could be applied to the rings 
of A and lead current from A into an entirely separate external 
circuit. As the armature rotates, an equal E. M. F. is generated 
in each coil but the currents in the respective circuits vary with 
the resistances of these circuits and are entirely independent of 
each other, in fact, the machine is electrically equivalent to two 
separate and distinct machines, the only connection between the 
two being that they generate equal E. M. F.s of equal periodicity. 
If the E. M. F. curves of the two coils be plotted on a common 
axis of time, it will be seen that their maxima occur at a constant 
phase difference of 90°. Since the machine thus generates two 
distinct currents of different phases, it is called a two-phase or a 
di-phase alternator. 

Theoretically, other coils could be inserted midway between 



ELECTRO-MECHANICS. 



521 



those of Fig. 341 and still others between these, each with its own 
collector rings and each supplying a separate external circuit with 
current differing in phase from the currents from the other coils. 
Practically, the distinct windings of such alternators rarely exceed 




Fig. 341. 

three. Those which generate more than one current are designated 
as polyphase; those which generate but one are, in contra-distinc- 
tion, called single phase. 

It can be shown that to generate these polyphase currents it is 
not necessary that the windings for each phase should be entirely 
separate. For example, as shown in Fig. 342, by tapping a ring- 




Fig. 342. 

wound armature at four points 90° apart and by connecting each 
of the tapping wires to a collector ring, we obtain a two-phase 
alternator. At the instant shown in the diagram the leads A are 
carrying the entire current, the current in the leads B being zero 
since the points to which their tapping wires are connected are 



522 



ELEMENTS OF ELECTRICITY. 



momentarily at the same potential. When, however, the armature 
has turned through an angle of 90°, these conditions are reversed 
and the leads B will carry the entire current, while the current 
in A will be zero. 

While polyphase currents are used to a limited extent in a three- 
wire lighting system, their principal use, as will be explained in 
the following chapter, is for the operation of alternating current 
motors. 

645. Tri-Phase Alternators. — In its most general form, the 
armature of a tri-phase alternator carries three distinct windings 
spaced 120° apart and supplied with six collector rings by which 
currents can be distributed to three separate circuits. The E. M. 
F. generated by such an alternator is shown in Fig. 343, the sine 
waves being of equal amplitude but differing in phase by 120°. 

If the resistances of the three circuits are equal, then the cur- 
rents are also equal and the circuits are said to be balanced. In 
such a case the curves in Fig. 343 may be taken as representing 




Fig. 343. 

the currents also. Examination of this figure will show that at 
any point along the horizontal axis, the sum of the ordinates is 
zero. For example, at A and C where the current in one of the 
circuits is zero, the currents in the other two circuits are both 
equal and opposite, and at B and D where the current in one of 
the circuits is a maximum, the sum of the currents in the other 
two circuits is equal and opposite. It is therefore possible when 
the circuits are balanced to discard three collector rings and three 
lead wires, for whether the current goes out on one or on two wires, 
an equal current comes in on the remaining wires or wire. The 
arrangement of such a three-wire three-phase system is shown in 
Fig. 344. 



ELECTRO-MECHANICS. 



523 



Should the circuits not be balanced, it is still possible to reduce 
the number of leads and collector rings from six to four, the fourth 
wire serving as a common return for the excess current of the 
other three. 

646. Tri-Phase Delta Connection.— In Fig. 344, a represents 
diagrammatically a ring wound armature tapped at three points 
120° apart, each tapping wire terminating in a collector ring. 
These rings, A, B, C, for the sake of clearness are represented as 




Fig. 344. 

separated from their common axis. The same armature is repre- 
sented in b in a still more highly conventionalized form, the curved 
portions between the tapping wires being straightened out and 
the rings being drawn at the vertices of the resulting triangle. 
This diagram also shows the three leads running from these rings 
and the arrangement of lamps so as to produce a balanced system. 
On account of the shape of the diagram this is called a 
^-connection, sometimes also a mesh-grouping. At one instant 
the entire current flows out on A and returns through the lamps 
D and E; at another instant it flows out on C and returns 
through D and F; at still another it flows out on B and returns 
through E and F; at all others, a varying current flows through 
each lamp. 

At the instant represented in a, Fig. 344, the armature coils 
between B and C are sending current out by C, and the coils 
between A and C (except the few to the left of the neutral plane) 
are contributing to this current. The currents in these two por- 
tions of the armature windings do not reach their maxima simul- 
taneously but the total resultant current is a maximum when 
these component currents are equal which is the case at A, the 
60° phase in Fig. 343. The maximum current in the leads is 
therefore 2 sin 60° = V3 times the maximum current in one portion 



524 



ELEMENTS OF ELECTRICITY 



of the armature windings. The maximum E. M. F. between any 
two of the leads is, however, no greater than that in one portion 

of the armature windings. 

647. Tri- Phase Y- Connection. — Suppose that in addition to 
tapping the ring-wound armature in three points, as described 
in the preceding paragraph, we cut the winding at these points 
and connect the corresponding ends together as shown in Fig. 
345 a. The current entering at B (at the instant represented in 




Fig. 345. 

the diagram) flows to the common junction at the center where it 
divides, a portion going to A, the remainder to C. This arrange- 
ment, shown still more diagrammatically in b, is called a Y-con- 
nection, sometimes also a star grouping. 

The E. M. F. of the coils between B and a is now in series with 
that of those between a and A and of those between a and C, 
excepting in both cases the few turns to the left of the neutral 
plane. The maximum E. M. F. between the leads of b is therefore 
the sum of the E. M. F.s in two of the three portions of the arma- 
ture windings at the moment when the E. M. F. in the third 
portion is zero. This is represented by the double ordinate at A 
in Fig. 343. But A being at the 60° phase, this double ordinate 
is 2 sin 60° = V3, or the maximum E. M. F. between any two of 
the leads is v 7 3 times the maximum E. M. F. developed in a 
single portion of the armature windings. 

On the other hand, since at any one instant never more than 
two of the portions of the armature windings can combine in 
delivering current, and since these two portions are always in 
series, the maximum current in the leads is the same as the maxi- 
mum current in any one of these portions. 

It will be noted that in the A-connection the current is VS 
times the maximum of that in the armature coils, while in the 



ELECTRO-MECHANICS. 525 

Y-connection the voltage is V'S times the maximum of that in 
these coils. The power, IE, developed by the two arrangements 
is therefore the same. 

648. Transformation of Direct and of Alternating Currents. — 

We have seen that the secret of the electrical transmission of 
power is the employment of currents of high potential (Par. 502). 
On account of freedom from trouble caused by sparking at the 
commutator, it is true as a general statement that an alternating 
current can be turned out at a higher voltage than can a direct 
current. Whether the current produced by a generator be direct 
or alternating, it is often desirable to raise its voltage still higher 
before sending it out on the line, and whether this be done or not, 
it is almost always necessary at the distant end of the line to 
reduce the voltage to fit the standard machines or lamps with 
which it is to be used. In this transmission, therefore, a current 
must be stepped up at the sending station and stepped down at 
the receiving station. 

In the case of direct currents, this transformation is effected by 
motor generators (Par. 605). These machines are costly, their 
operation involves a considerable loss of power and they require 
as much attention as the generator itself. If power is to be dis- 
tributed among scattered buildings, a motor generator and an 
engineer would be required in each, also space for installation of 
the machine. On the other hand, these changes in alternating 
currents are made by transformers which are relatively inexpen- 
sive, require little or no attention and have an efficiency in some 
cases exceeding 98 per cent. They may be placed wherever 
needed and occupy but little room since they are usually mounted 
against a wall or upon a pole like a letter box. For these reasons, 
for the transmission of power to a distance, the alternating current 
has a great advantage over the direct. 

649. Transformers. — The principle of transformers was out- 
lined in Par. 431 but they are considered here again in order that 
some additional facts about their use may be brought out. That 
they rightfully fall under the heading of the present chapter, the 
following will show. An alternator is a machine which induces 
an alternating E. M. F. by rapidly varying the magnetic flux 
through a coil. From this point of view, a transformer is also an 
alternator, the E. M. F. in the secondary being induced by the 



526 



ELEMENTS OF ELECTRICITY. 



changing flux produced in it by the primary. Moreover, since the 
transformer has no moving parts (and is hence sometimes called 
static), there is no loss of energy in overcoming friction, etc., and 
by proper design the combined losses due to magnetic leakage, 
eddy currents, hysteresis and resistance may be reduced to less 
than two per cent, so that we may say that the transformer is the 
most efficient of machines. 

Transformers are of two types, the core or ring transformer 
(Fig. 204) and the shell transformer (Fig. 205). The shell trans- 
former is the more frequently used but, for the sake of clearness, 
the following diagrams represent ring transformers. 

In the actual construction of the shell transformer, the coils are 
usually wound in separate portions which are thoroughly insulated 
and then sandwiched together, after which they are placed in a 
form and the laminated iron punchings of which the shell is com- 
posed are built up around them. The completed coils are then 
put in an iron case which is usually filled with oil. This serves a 
double purpose; it aids the insulation of the coils, prevents the 
penetration of moisture into the wrappings and prevents excessive 
heating of the coils. In some of the larger transformers, the oil 
itself is cooled by water circulating in pipes which pass through 
the oil. In others, the oil is omitted and cooling is brought about 
by currents of air driven over the coils. 

If a current be sent through the primary of a transformer, it 
will produce in the core a certain number of lines of force. These 
lines, as shown in Fig. 346, penetrate every turn of the coils in 



H 



Fig. 346. 

both primary and secondary. An equal E. M. F. is therefore 
induced in every turn. If this E. M. F. be e, and if there be N' 
turns in the primary and N" in the secondary, the E. M. F. in the 
primary is E' = N'e, that in the secondary is E" = N"e, whence 

E' : E"=N' : N" 



ELECTRO-MECHANICS. 



527 



or, as already shown (Par. 431), the E. M. F.s in the two coils are 
to each other as the number of turns in the respective coils. 

650. Operation of Transformer. — In Par. 431 it was shown 
that the work done in the primary of a properly designed trans- 
former is equal to that done in the secondary. It follows from 
this principle that the current in the primary varies with the 




Fig. 347. 

current in the secondary and that when the secondary circuit is 
open there should be no current in the primary. This can be 
shown experimentally by the arrangement shown in Fig. 347. 
With the switches in the secondary circuit open, the ammeter in 
the primary circuit indicates the merest trace of a current. Reflec- 
tion will show that the primary, a coil of small resistance wrapped 
about a soft iron core, is nothing more nor less than a choke coil 
as described in Par. 621, and that the current is cut down by the 
choking effect. The small current which does get through, the 
"no load current, " is just sufficient to maintain the magnetic flux. 

If now one of the switches in the secondary be closed, the 
ammeter will indicate a current through the primary. If a second 
switch be closed, the current through the primary is doubled ; if a 
third switch be closed, it is trebled, in other words, the current 
through the primary adjusts itself to conform to the current in 
the secondary, or, the primary acts as an automatic valve and 
permits only so much current to flow through it as is needed to 
supply the demands of the secondary. 

This very remarkable property may be explained as follows. 
When an E. M. F. is impressed upon the primary, the secondary 
circuit being open (Fig. 346), a current flows and produces within 
the primary a magnetic flux. The lines of force, as shown by the 
arrowheads, travel around the magnetic circuit and enter the 
primary from below. This sets up an induced E. M. F. in the 
primary opposite to the actual E. M. F. (Par. 421) and conse- 



528 



ELEMENTS OF ELECTRICITY. 



quently cuts down the current in the primary. An E. M. F. is also 
set up in the secondary but produces no current since this circuit is 
open. When, however, the secondary circuit is closed, a current 
flows as indicated by the arrowhead. This current produces lines 
of force opposite in direction to those from the primary, that is, it 
diminishes the number of lines from the primary (Par. 418, b). 
This in turn diminishes the choking effect and allows a larger 
current to flow through the primary. 

From the facts brought out above it will be seen that in any 
given transformer the voltage in the secondary varies directly 
with the voltage in the primary; on the other hand, the current 
in the primary varies directly with the current in the secondary; 
in other words, the primary determines the voltage; the secondary 
determines the current. 

651. Connection of Transformers. — On account of the choking 
effect described in the preceding paragraph, transformers are not 
connected in series but in parallel. Fig. 348 represents an alter- 



am 



ef 



jot 



Fig. 348. 



nator delivering high potential current to two mains and through 
transformers connected in parallel distributing energy from these 
mains to the stations A and B. 

652. Auto-Transformers. — The transformers described in the 
preceding paragraphs are used when the voltage in the primary 
is to be very materially changed, as for example when it is to be 
increased or diminished tenfold, or, as a minimum, when it is to 
be doubled or halved. Smaller changes in voltage may be made 
by means of resistance, but this we have shown to be wasteful. 
A better method is to use the so-called auto-transformer, shown 
diagrammatically in Fig. 349. This is a transformer in which the 
primary and the secondary coils are combined in one. In prin- 
ciple it does not differ from the ordinary transformer. As explained 
in Par. 649, when a current is sent through the primary coil, an 
equal E. M. F. is developed in every turn. The E. M. F. in the 



ELECTRO-MECHA NICS. 



529 



secondary therefore varies directly with the number of turns 
tapped by it. In the diagram, the secondary is used to step down 
the voltage in the primary. If the current were delivered to the 




Fig. 349. 

secondary and drawn from the primary, the voltage would be 
stepped up. 

653. Rectification of Alternating Current. — An alternating 
current may be rectified in several ways. It has already been 
shown (Par. 556) how it may be rectified at the point of origin by 
means of a commutator. It is, however, frequently desirable to 
transmit the current to a distance as alternating and to rectify 
it at the receiving station. In this case it may be rectified by (a) 
mechanical means, or by (b) electro-chemical means. 

An alternating current is rectified mechanically by means of a 
synchronous converter, also called a rotary converter. Briefly ex- 
plained, this is a generator with both commutator and collector 
rings. The alternating current is delivered to the collector rings 
and the machine operates as a motor. While so operating, direct 
current is drawn from the commutator. 

Alternating current may also be rectified mechanically by a 
motor-generator (Par. 605), the motor being driven by the alter- 
nating current and direct current being drawn from the com- 
mutator of the generator at the opposite end of the shaft. 

The electro-chemical rectifiers are of several kinds. In one, the 
current is passed through a cell containing electrodes of aluminum 
and of lead or steel, the aluminum having the property of per- 
mitting the current to pass when it is the cathode but suppressing 
it when it is the anode. Allied to this is the mercury arc rectifier 
which will now be described. 

654. The Mercury Arc Rectifier. — In the description of the 
mercury vapor lamp (Par. 527), it was shown that the resistance 



530 ELEMENTS OF ELECTRICITY. 

to the passage of the current was confined mainly to the surface 
of the negative electrode and was so great that several thousand 
volts were required to break it down, but that once that it had 
been broken down, a current could be maintained by a small 
voltage provided that this current did not fall below a certain 
minimum. If it fell below this, the negative electrode resistance 
was re-established and the current was interrupted. 

This principle is utilized in the mercury arc rectifier, an appara- 
tus for the conversion of alternating currents into the relatively 
small direct currents such as are employed in charging the smaller 
storage batteries. It may be used with either single phase or 
polyphase currents. Its operation will be understood from the 
following. Fig. 350 represents diagrammatically one of these 




Fig. 350. 

converters. It consists of a pear-shaped exhausted glass globe 
of about nine inches in diameter. Through its top extend the 
terminals A and B which connect on the interior with the iron 
electrodes C and D. A third terminal enters below and connects 
with the mercury electrode E. Suppose that desiring to charge 
the storage battery F by means of current from an alternator M, 
we should make connections as shown on the right of the diagram. 
No current can flow in either direction until the negative electrode 
resistance at either D or E be broken down. Suppose that as 
explained below this resistance be broken down at E. Current 
will now flow through the circuit in the direction BDEF but will 
continue to flow for only a small fraction of a second. As soon 
as the voltage between D and E drops to about ten volts, the 



ELECTRO-MECHANICS. 



531 



resistance at E is re-established and the current is interrupted. 
When the E. M. F. reverses, no current can flow, for the resistance 
at D has not yet been broken down. We see then that this ar- 
rangement could not be used. Now suppose a direct current 
generator G to be connected as shown on the left of the diagram. 
When the resistance at E has once been broken down, direct 
current from G will flow steadily in the direction ACEF. If now 
the alternator be turned on, the alternating E. M. F. in the 
direction BDE can send a current through the circuit because the 
direct current from G, by preventing the resistance at E from 
reasserting itself, keeps open the road through E, but the alternate 
impulses in the reverse direction can send no current since the 
resistance at D prevents. It is thus seen that by such an arrange- 
ment the alternating current from one-half of each cycle could be 
used to charge the battery. 

The illustration above is purely hypothetical but is intended 
to bring out the fact that if in any manner the resistance at the 
negative electrode can be kept broken down, then the apparatus 
becomes selective in its operation and permits current to pass in 
one direction but not in the other, in other words, it becomes a 
rectifier. 

655. Rectification of Single Phase Current. — The arrangement 
of the converter to rectify a single phase current is shown in Fig. 
351. The leads from the alternator M terminate in the electrodes 




Fig. 351. 

C and D, but at A and B branches are thrown off which include 
the inductance coils G and H and unite at J. To one side of the 
electrode E there is an auxiliary mercury electrode F which is 



532 ELEMENTS OF ELECTRICITY. 

connected through a resistance R with the wire from A to G. 
The globe is mounted so that it may readily be tilted. 

To charge a storage battery, the battery is connected between 
E and J as shown. The globe is then tilted until the mercury in 
E connects with that in F. At this instant the current passes 
through the path MARFEJHBM. The globe is now released 
and as the thread of mercury between E and F is broken, an arc 
is produced, some of the mercury is ionized and the vapor in the 
globe is thereby rendered a conductor. The path of the current 
is now MACEJHBM, but the E. M. F. acting in this direction 
soon dies down and then reverses, that is, acts in the direction 
MBD. The inductance of the coil H now comes into play and 
prolongs the current through H, a momentary current flowing 
around the circuit JHBDEJ. Before this delayed current has 
died down to the point where the resistance of E is re-established, 
it is picked up by the growing E. M. F. in the direction MBD, the 
circuit now being MBDEJGAM. At the next reversal, the in- 
ductance of the coil G comes into play, and so on, these induced 
delayed currents fulfilling the part of the direct current described 
in the preceding paragraph and keeping the path through E open. 

656. Comparison of Alternating and Direct Currents. — Alter- 
nating current generators, since they require no commutator, are 
somewhat cheaper to construct than those for direct current, but 
this may be counterbalanced by the cost of the separate field 
exciter. The great advantage of alternating currents is the ease 
with which they may be transformed and the simplicity and the 
efficiency of the static transformers used for this purpose. On 
the other hand, they can not be used in electrolytic work nor in 
charging storage batteries and alternating current motors fall 
behind direct current motors both in efficiency and in speed 
regulation. While most incandescent lamps operate equally well 
with either kind of current, the arc lamp mechanism for alternating 
currents is not so satisfactory as that for direct currents. As a 
general statement therefore, alternating current is most suitable 
where power is to be transmitted to a distance; in all other cases 
direct current is to be preferred. 



ELECTRO-MECHANICS. 533 



CHAPTER 45. 

ALTERNATING CURRENT MOTORS. 

657. Alternating Current Motors. — The electrical conditions 
encountered in motors designed for use with alternating currents 
are particularly complex. The interaction of the flux of the field 
coils and that of the armature coils, one or both of which may be 
shifting, the inductance, hysteresis and eddy currents necessarily 
developed in a machine in which alternating currents flow through 
coils embracing soft iron cores, render the mathematical treatment 
of the problem more intricate than is desirable in an elementary 
text book. In the following pages therefore, we can do no more 
than glance at the fundamental principles of a few of the simpler 
forms. 

658. Classes of Alternating Current Motors. — Alternating cur- 
rent motors are usually classed under the following heads: 

(a) Series motors. 

(b) Synchronous motors. 

(c) Repulsion motors. 

(d) Induction motors. 

The distinction between these will be brought out as we proceed. 

659. Series Motors. — In Par. 604 it was shown that changing 
the direction of the current supplied to a shunt motor did not 
alter the direction of rotation. The same could have been shown 
for the series motor. At first sight, therefore, it would seem that 
whether supplied with direct or with alternating current, these 
motors would operate equally well. In the case of the shunt 
motor however, the inductance of the field coils is much greater 
than that of the armature coils. The current through the field 
coils therefore lags much more than that through the armature 
(Par. 617). The torque is a maximum when the armature current 
and the field flux reach their maxima simultaneously, but since 
the field and the armature currents differ in phase, but little power 
is developed. The shunt motor, therefore, is not used with alter- 
nating currents. 



534 



ELEMENTS OF ELECTRICITY. 



In the series motor, the field and armature coils being in series, 
there can be no phase difference and the above objections do not 
apply. When used with single phase alternating currents, series 
motors develop great starting torque and possess the advantages 
and disadvantages described in Pars. 602 and 603. They are 
therefore largely used as railway motors. The A. C. motors 
differ from the D. C. motors in certain minor arrangements by 
which the tendency of the A. C. machine to excessive sparking is 
reduced. Also, as in all other A. C. machines, the field cores must 
be laminated. 

660. Synchronous Motors. — Suppose Fig. 352 to represent a 
rectified portion of the alternator shown in Fig. 337. AB repre- 
sents the field which is excited by direct current and whose polarity 




Fig. 352. 

therefore does not vary. CD represents a portion of the revolving 
armature, the coils supplied with alternating current from a 
distant source. At the instant shown in the diagram, it will be 
seen that each pole of the armature experiences a force which 
tends to move CD from left to right. If CD does not move, it 
will at the next reversal of the current be urged in the opposite 
direction, or from right to left. Suppose it begins to move from 
left to right. If before the moving coil E arrives beneath F, the 
current through E reverses, the polarity of E also reverses and 
E will be driven back from F, in other words, the movement of 
CD will be checked. If E passes under F without reversing, it 
will be pulled back as soon as it begins to emerge on the other 
side. If it reverses as it passes under F, it will be pushed ahead. 
The frequency of the alternating current supplied to the arma- 
ture being constant, the relative positions of the fixed field poles 
and the rotating armature coils at the instant when the current 



ELECTRO-MECHA NICS. 



535 



in these latter reverses depends upon the angular speed of the 
armature. The effect of variation in this speed can be shown 
graphically as follows. In Fig. 353 A B represents the fixed field, 
and a, b and c represent the successive positions of an armature 
coil moving at three different speeds. If the armature be rotated 



' m//////// m^m 



f 



J^L_R_F1_J^_M R 



I fiL 



'W^W^W 



b 



M 



M 



M 



Jll 



M 



Fl 






Fig. 353. 

slowly, the angular distance between reversals is small; if it rotates 
rapidly, this angular distance is large. In a, the armature is 
turning slowly and the polarity of the coil reverses when the coil 
has travelled through less angular distance than that separating 
the field poles. In b, it is turning rapidly and the reversals occur 
at angular distances apart greater than that between the field 
poles. In c, the reversals occur at the same angular distance 
apart as that separating the poles. In this last case, the armature 
coil passes over the distance between two successive north poles 
of the field in the same time that a coil of the distant alternator 
supplying current to the armature passes over the distance be- 
tween two successive north poles of its field, in other words, the 
armatures of the motor and of the alternator rotate in electrical 
synchronism. 

For the sake of clearness only forces of attraction are represented 
in these diagrams. It is seen at a glance that only in the case of 



536 ELEMENTS OF ELECTRICITY. 

the synchronous rotation is the torque the same in direction for 
the successive positions of the rotating coil. If, therefore, an 
alternator be brought up to synchronous speed and then supplied 
with alternating current, it will continue to rotate. Such machines 
are called synchronous motors. They differ in a few minor details 
from alternators. Either the field or the armature may revolve 
and they may be driven by either single phase or polyphase 
currents. 

661. Operation of Synchronous Motors. — A serious objection 
to the single phase synchronous motor is that it can not of itself 
start from rest. An auxiliary motor is required to bring it up to 
synchronous speed before the current is turned on. The polyphase 
machines will start up of themselves, but even with these it is 
usual to employ an auxiliary starter. 

Since these motors must maintain synchronous speed, it follows 
that their speed does not vary with variations in the load. The 
question then arises how is the supply of power varied to meet 
the different demands made upon it. The force on an inductor 
of the armature being I. H. I (Par. 591) varies directly as the 
current. The current varies as the difference between the im- 
pressed E. M. F. and the back E. M. F. (Par. 593). The impressed 
E. M. F. is delivered by the alternator and is constant. The back 
E. M. F. varies with the speed of rotation of the armature, hence 
also is constant. If these two E. M. F.s reached their maxima 
and minima simultaneously, in other words, if they were in phase, 
the difference between them, and hence the current, would be a 
minimum. If, however, the armature coils should fall back a few 
degrees in angular position, still preserving synchronous rotation, 
the two E. M. F.s would no longer be in phase, their difference 
would increase and a greater current would flow. When, therefore, 
a load is thrown on a synchronous motor, the armature drops 
back a few degrees and thus exerts a greater torque. If the load 
be excessive, the machine is thrown out of synchronism and stops. 

662. The Repulsion Motor. — The repulsion motor, shown 
diagrammatically in Fig. 354, consists of an ordinary D. C. 
armature placed in a field produced by a single phase alternating 
current. As the field alternates, an E. M. F. is induced in every 
coil in the armature except in the two at the opposite ends of the 
horizontal diameter. The direction of these E. M. F.s for an in- 



ELECTRO-MECHANICS. 



537 



creasing flux from N is indicated by the arrowheads in the dia- 
gram. No current is produced since the E. M. F.s in the two 
halves of the armature are equal and opposed. If a brush be ap- 
plied to the commutator so as to touch two adjacent segments, a 
current will be produced in the coil thus short-circuited. If the 




brushes be applied to the terminals of the coils A and B, the 
resulting flux in these coils will be opposite and parallel to the 
field and hence no torque will be developed. If, however, the coils 
D and E be short-circuited, the flux in these coils, as shown in 
the diagram, will be oblique to the field, D will be repelled from 
N and E will be repelled from S and clockwise rotation will ensue. 
When the field is reversed, the flux in the coils is also reversed 
and the rotation will continue in the same direction. As thus 
described, only the coils in the positions D and E contribute to 
the torque. If the brushes be enlarged so as to short-circuit a 
number of adjacent coils, all of these coils will contribute to the 
turning moment. Finally, if the brushes be connected as shown, 
currents will flow through the remaining coils and the torque will 
be correspondingly increased. 

It will be noted that there is no direct electrical connection with 
the armature of this machine and that the currents are produced 
by induction. It is therefore a true induction motor. 

663. Principle of Induction Motor. — The principle of the 
induction motor will be understood from the following. 

SNS, Fig. 355, represents a series of magnetic poles, alternating 
in polarity and moving steadily from right to left as indicated by 
the arrow. Beneath these there is what may be compared to a 



538 



ELEMENTS OF ELECTRICITY. 



copper ladder with heavy copper rungs. Consider the opening 
ABCD in this ladder. At the instant shown it is penetrated by 
the lines of force from N, but as N is moving off to the left, the 
number of lines embraced is decreasing and there is therefore 
induced a clockwise current in the direction ABCD (Par. 421). 
In the adjacent opening ABEF, the number of lines embraced 
is increasing and there is therefore induced a counter-clockwise 
current in the direction ABEF, that is, the E. M. F. in the copper 
surrounding both of these openings produces a current from A to 




O fO aQ — 02 o o 



Fig. 355. 

B. Since AS is a conductor carrying a current and placed in a 
magnetic field, it experiences a force urging it to follow along after 
the moving pole (Par. 352). In a similar manner it can be shown 
that the rungs under the south poles are also urged to the left. 
Reflection will show that this movement is also a consequence of 
Lenz's law (Par. 430). 

Although the induced E. M. F. be small, the currents in the 
copper rungs are, on account of the low resistance, very large and 
the force I. H. I on the rungs (Par. 356) is also large. 

Suppose now the copper ladder to be bent into a cylindrical 
shape and fixed upon an axis like a squirrel cage (Fig. 356), and 
suppose the moving poles to be formed into a ring surrounding this 
cylinder, and their movement of translation to be converted into a 
movement of rotation. Corresponding rotation will be produced 
in the squirrel cage, which by a suitable pulley or by gearing could 
be made to do mechanical work. We have thus produced rotation 



ELECTRO-MECHANICS. 



539 



in the cage by rotating the magnetic field about it, but the thought 
arises at once that the energy expended in rotating the field 
might better have been applied to the cage direct. However, it 
will now be shown that it is possible to produce a rotating field 
without resorting to mechanical rotation. 




Fig. 356. 

664. Production of Rotating Field. — Suppose Fig. 357 to repre- 
sent a ring wound stationary iron frame and suppose there are 
connected to the winding at points 90° apart the leads CC and 
DD' from a two phase alternator similar to the one shown in 
Fig. 341. Suppose we start with the armature in the position 




shown in that figure. At this instant the current in the leads CC 
is a maximum and that in DD r is zero. Application of the right 
hand rule shows that the current entering at C and leaving at C 
produces a south pole at C and a north pole at C\ The current 



540 ELEMENTS OF ELECTRICITY. 

entering at C now begins to decrease, while an increasing current 
starts in at D. Currents leave by C" and D ; and a north pole is 
produced between C and D f . 

When the current at C has dwindled to zero, the entire current 
enters at D and leaves by D'. A north pole is therefore produced 
at D'. 

Without carrying this explanation farther, it is seen that during 
one complete cycle a north pole starts at C and travels in a 
clockwise direction entirely around the iron frame, a corresponding 
south pole keeping pace at the opposite end of the diameter of the 
ring. The effect is therefore the same as if the frame work had 
held a pair of permanent magnetic poles and had been rotated 
through L 360°. In the actual case, however, there has been no 
mechanical motion and no waste of energy in overcoming friction, 
such as would have occurred had the heavy iron frame been 
rotated. A squirrel cage placed inside of this ring would have 
been rotated by the rotating poles. 

The rotating field described above was produced by a two-phase 
current. It may also be produced by a tri-phase current. 

665. The Induction Motor. — The induction motor is based 
upon the foregoing principles. The rotating cage, although it 
resembles the armature of other motors, is not strictly an armature 
since it has no electrical connection with the power circuit. It is 
therefore called the rotor, the surrounding magnetic field being 
called the stator. This is the usual arrangement but it is quite 
possible to have the field the rotating member. 

The inductors are of copper as described above, and in order to 
insure penetration by the lines of force of the field, the interior 
of the rotor is built up of laminated iron (Par. 565), in fact, the 
copper inductors are generally embedded in slots in this laminated 
core. The stator is likewise laminated and, instead of being ring 
wound as described in the preceding paragraph, it is wrapped 
somewhat as shown in Figs. 337 and 339. 

If the rotor revolved synchronously with the rotating field, 
there would be no cutting of lines of force by the inductors, hence 
no induced current and no torque developed. In order then to 
develop torque the rotor must run below synchronism. It would 
therefore seem that the slower the rotor turned the greater would 
be the torque, but this is not correct. Examination of Fig. 355 
will show that as the pole N moves over the interval ABEF, an 



ELECTRO-MECHANICS. 541 

upward flux is produced, that is, a flux tending to demagnetize N. 
The force on an inductor is I. H. I (Par. 356), but when the speed 
falls below a certain point, the field H is demagnetized more 
rapidly than / increases and the total force therefore falls off. If, 
therefore, an increasing load be applied to one of these motors, it 
will slow down until the maximum torque is developed, after 
which, if the load be further increased, it will come to a stop. 

If one of these motors is to start from rest under load, as for 
example in operating an elevator, it is desirable that the maximum 
torque should be exerted at starting. This may be attained by 
constructing the rotor so that the resistance of the inductors may 
be varied. The resistance is introduced at starting and the cur- 
rents through the inductors are thus kept down so that the de- 
magnetizing effect described above will not be too great. As the 
motor gathers headway, this resistance may be cut out. 



HIGH POTENTIAL. 543 



PART VI. 
HIGH POTENTIAL. 



CHAPTER 46. 

DISCHARGE OF ELECTRICITY THROUGH GASES. 

666. High Potential. — The two following chapters, with which 
we conclude this book, treat of the discharge of electricity through 
gases and of electrical oscillations. While these subjects stand 
somewhat apart from the divisions which we have hitherto con- 
sidered, they can riot be said to be very intimately interrelated, 
and they are here classed under one heading mainly because 
their most characteristic phenomena are usually produced by 
the use of high voltages. The title "high potential" must not 
therefore be regarded as descriptive but rather as used to avoid 
the comprehensive but still more indefinite designation ' 'mis- 
cellaneous.' ' 

667. Conductivity of Gases. — Gases are ordinarily the most 
perfect of non-conductors. In the list of these bodies given in 
Par. 20, air was placed at the foot. However, under certain con- 
ditions described below (Par. 680) their conductivity can be 
greatly increased. Although some of these conditions have been 
known for upwards of fifty years, it is only within comparatively 
recent times that this subject has been systematically investi- 
gated, and as a result of these studies much light has been thrown 
both upon the mechanism of conduction and upon the ultimate 
nature of electricity itself. 

668. Discharge Through Moderate Vacua. — Fig. 358 represents 
the arrangement already described in Par. 525. AS is a long 
glass tube into each end of which is sealed a platinum wire ter- 
minating on the inside in a small disc. The platinum wires are 
connected to the opposite sides of the spark gap G H of an indue- 



544 



ELEMENTS OF ELECTRICITY. 



tion coil. An air pump is attached to a small tube blown in one 
side of the larger tube and the air is gradually exhausted. At 
first, the sparks produced by the coil leap across the gap GH, 
but as the air is exhausted from the tube these sparks cease and 
a flickering light, like summer lightning, appears on the inside. 



CATHODE 



anode: 




Fig. 358. 

If the exhaustion be carried a little farther, or to a pressure 
corresponding to about an inch of mercury, a luminous column, 
the positive column, extends the entire length of the tube between 
the anode and the cathode. The spark gap may now be very 
materially decreased without a spark passing, thus showing that 
the conducting power of the gas within the tube has been greatly 
increased. 

669. Effect of Magnetic Field on Positive Column. — If while 
the discharge is taking the form of the positive column the tube 
be placed in a crosswise magnetic field, the column is deflected 
for a portion of its length. Thus, if a horseshoe magnet be placed 
as shown in Fig. 358 so that the tube is penetrated at right angles 
by a magnetic field from rear to front, the portion of the column 
between the poles of the magnet will be bent upward as indicated 
by the dotted lines. Application of the left hand rule (Par. 352) 
will show that in this respect the column behaves as if it were a 
flexible conductor carrying a current. 

670. Discharge Through High Vacua. — If the exhaustion of 
the tube described in Par. 668 be continued, when the pressure 
has been reduced to about that of two millimeters of mercury, 
the following changes are observed. The surface of the cathode 
is covered with a thin luminous layer. Adjoining this there is a 



HIGH POTENTIAL. 



545 



dark space C (Fig. 359), the Crookes dark space, which enlarges 
as the pressure diminishes, and adjoining this space there is a 
luminous region D, the negative glow. Beyond this there is a 
second dark space F, the Faraday dark space, followed by the 
positive column E which is now broken up into striae, transverse 

a c n f e: b 



o-Mtimm wmm % 1 1 i n s i i wm^ 

Fig. 359. 
luminous discs. A potential sufficient to produce in air a spark 
one-eightlr of an inch in length will now cause a discharge through 
a tube twenty inches long. Tubes exhausted to this extent are 
called Geissler tubes. 

If the exhaustion be carried to about one-millionth of an 
atmosphere, the tube is called a Crookes tube. The luminous 
spaces entirely disappear, the Crookes dark space spreading 
throughout the tube, but the glass itself now begins to phosphor- 
esce with a color which varies with its composition. Soda glass 
glows with a fine green color; lead glass with a pale blue. The 
resistance is now much greater and increases rapidly so that if 
the exhaustion be carried slightly farther it becomes no longer 
possible to send a discharge through the tube. 

671. Cathode Rays. — It was discovered by Crookes that the 
phosphorescence of the glass tube described in the preceding 
paragraph is produced by certain invisible radiations proceeding 




Fig. 360. 

from the cathode, and these have accordingly been named cathode 
rays. It may be shown that they leave the cathode at right 
angles to the latter's surface. In the V-shaped Crookes tube 
shown in a, Fig. 360, whether A or B be used as the anode, only 
B, the arm up which the cathode points, will phosphoresce. 



546 ELEMENTS OF ELECTRICITY. 

If the cathode be given a concave shape, a piece of platinum 
foil placed at the focus may be raised to a red heat by the rays. 
Many substances, even when not highly heated, fluoresce or 
emit brilliant light when placed in the path of these rays. 

672. Nature of Cathode Rays. — Investigations lead to the 
belief that the cathode rays consist of minute material particles 
carrying electrical charges and moving with a velocity so great 
that they cause the bodies upon which they strike to become 
heated and to emit light or fluoresce. These particles have been 
variously named corpuscles, electrons and negative ions. 

In the Crookes tube shown in b, Fig. 360, a mica cross B is 
mounted upon the anode A and when the tube is in operation a 
distinct shadow of this cross appears upon the phosphorescent 
background at D. B therefore screens the glass from the rays 
from C. Since B is transparent, the cathode rays are not of the 
nature of ordinary light. 

If, instead of the cross, a very delicate little paddle wheel be 
mounted at B and so placed that the rays from C strike upon 
the vanes of one side only, it will take up a motion of rotation 
as if it had been bombarded with small particles from C. 

673. Effect of Magnetic Field on Cathode Rays. — The cathode 
rays are deflected by a magnetic field. In the Crookes tube 





Fig. 361. 

shown in Fig. 361, a diaphragm B with a narrow slit is placed in 
front of the cathode. Beyond this diaphragm and lying along 
the axis of the tube is a vertical sheet of mica coated with chalk. 
The narrow beam of rays through the slit causes in this chalk 
a bright line of fluorescence CD. If now a horseshoe magnet be 
placed as shown in Fig. 358, the field running from rear to front, 
the beam of rays will be deflected in the same direction as the 
positive column (Par. 669). There is, however, a great difference 
in the two cases. The positive column is simply deflected as it 
passes through the field and beyond this field returns to its original 
direction; the cathode rays, after passing beyond the field, continue 



HIGH POTENTIAL. 



547 



in their deflected direction and terminate upon the side of the tube 
attf. 

674. Effect of Electric Field Upon Cathode Rays.— Cathode 
rays are also deflected by an electric field. Thus, if the tube shown 
in Fig. 361 be placed between two parallel metal plates, one above 
and the other below, and if the upper plate be charged positively, 
the rays will be deflected upward in the direction CE. The con- 
clusion is that the electrons, or little particles of which the cathode 
rays are composed, carry negative charges and are consequently 
attracted by the positively charged and repelled by the negatively- 
charged plate. 

The same conclusion might have been drawn from the deflec- 
tion produced in the cathode rays by a magnetic field. Since 
these rays, although moving in opposite direction, were deflected 
in the same direction as the positive column, they must have 
constituted a current of negative electricity. 

675. Nature of Charge Carried by Electron. — The correctness 
of the above conclusion that the electrons carry negative charges 




o H 



Fig. 362. 

is experimentally confirmed as follows. In the two-chambered 
Crookes tube shown in Fig. 362, B is a metal diaphragm pierced 
with a narrow slit and together with A constituting the anode. 
C is the cathode. The side tube D contains a condenser con- 
sisting of a metal cylinder with a narrow opening at F and a con- 
nection at G by which it may be grounded, and within the cylinder 
but insulated from it a second cylinder with a terminal at II. An 
electrometer is connected to this terminal . Normally , the cathode 
rays pass through the slit in the diaphragm and strike at E where 
they* produce a luminous spot. By means of a magnet these rays 



548 ELEMENTS OF ELECTRICITY. 

are deflected. The instant that they are bent enough to enter 
the opening at F, the electrometer indicates that the inner cylinder 
has received a negative charge. 

676. Positive Rays. — If the cathode of a Crookes tube be 
pierced with small holes, luminous rays passing through these 
holes will be seen at the back of the cathode. These are found 
to consist of positively-charged ions and are accordingly called 
positive rays, sometimes also canal rays. 

677. Lenard Rays. — While the cathode rays do not penetrate 
the Crookes tube in which they are produced, Lenard found that 
if a small window of aluminum foil be let into the side of the tube, 
the effect of the rays could be detected for a distance of several 
inches in the air on the outside. Since the fact that these rays 
apparently pass through metal appears contrary to the theory 
that they consist of small material particles, these exterior rays 
were at first considered to be something different and were called 
Lenard rays. It is now known that they are identical with cathode 
rays. It is thought that the cathode rays on the interior of the 
tube do not actually penetrate the aluminum but strike it with 
such energy that the percussion drives off ions from the outer 
surface. 

678. X-Rays. — In addition to heating the objects upon which 
they fall, the cathode rays cause these objects to emit rays of a 
very remarkable penetrative power. Roentgen accidently dis- 
covered this fact in 1895. He noticed that a covered photographic 
plate in his laboratory became fogged by the rays from a Crookes 
tube with which he was working. It was known that the effect 
of the Lenard rays extended only a few inches beyond the tube 
and he realized that he was dealing with an unknown form. He 
therefore designed then as X-rays, though later, in his honor, 
they were called Roentgen rays. 

They travel with the velocity of light, penetrate all bodies to 
some extent, are not reflected or refracted by those substances 
which reflect or refract light and are unaffected by electric or 
magnetic fields. Their penetration into the metals varies in- 
versely as the atomic weights of these metals. Lead, whose 
atomic weight is 207, is therefore the metal most frequently used 
as a screen for these rays. 

They excite powerful phosphorescence in many substances. 
Advantage is taken of this in the fluoroscope. This consists of a 



HIGH POTENTIAL. 



549 



light-proof frame shaped like the frustum of a pyramid. Over 
the larger end is spread a cardboard coated with barium platino- 
cyanide. The smaller end of the frustum is arranged so as to be 
applied to an observer's face as shown in Fig. 363. When exposed 
to the X-rays, the barium salt glows with a yellowish color and 
to the observer the effect is as if he were looking through a frosted 
glass window of that color. If the hand be interposed between 
the source of the X-rays and the fluoroscope and be applied to 
the coated cardboard, the X-rays penetrate the flesh more easily 
than they do the bones and the outline or shadow of the bones 
is clearly seen. This instrument is used in surgery in the examina- 
tion of fractures, location of foreign bodies, etc. 




Fig. 363. 

X-ray photographs or sciagraphs (shadow pictures) are made 
in a similar manner. The sensitive plate enclosed in its holder is 
usually placed on a table, the patient placing immediately above 
the plate the part of his body to be photographed. Exposure to 
the rays is then made and the plate is developed. In this way the 
greatest steadiness is secured. 

In making these sciagraphs a special form of Crookes tube, 
a so-called focusing tube, is used. As shown in Fig. 363, the cathode 
is concave and the anode located at its focus is a flat plate of 
platinum inclined at an angle of 45° to the cathode rays. The 
X-rays thus emanate from a small area and more clear-cut 
shadows are produced. 

These rays are particularly destructive to cells. They are 
therefore used in medicine for the treatment of superficial forms 
of cancer, tuberculosis and skin diseases, but they are not selec- 
tive and destroy the healthy as well as the diseased, producing 
burns which are very difficult to heal. 



550 ELEMENTS OF ELECTRICITY. 

679. Becquerel Rays. — In 1896 Becquerel in investigating the 
properties of phosphorescent bodies discovered that the compounds 
of the metal uranium emitted rays which partook of the nature 
of both the cathode rays and the X-rays. It was soon found that 
these Becquerel rays were not confined to uranium compounds 
but were produced by other substances. Those bodies which 
emit these rays are said to be radio-active. 

The principal ore of uranium is the oxide, pitch blende. The 
Curies found that the residue left after extracting the uranium 
from this ore was more radio-active than the uranium itself, and 
in 1898 they succeeded in separating from this residue a compound 
of a newelement. radium, whose radio-activity was over a mil- 
lion times greater than that of uranium. Radium is known to 
be a metal chemically allied to barium. It exists in such minute 
quantities that from a ton of the ore only about two-tenths of a 
gram of the impure chloride or bromide is obtained. Associated 
with it are polonium and actinium, two still rarer metals possessing 
similar properties. 

The Becquerel rays are complex but by passing them through 
a magnetic field they may be resolved into three types called 
the alpha, the beta and the gamma rays, respectively. The alpha 
and the beta rays are deflected, but in opposite directions; the 
alpha rays being positive rays, the beta rays being negative or 
cathode rays. The gamma rays are unaffected by the magnetic 
field and are allied to, if not identical with, the X-rays. They 
have almost incredible penetrative power, being able to penetrate 
upwards of a foot of solid iron. 

680. Increase of Conductivity of Gases. — While, as already 
stated, the conductivity of a gas is normally very small, there 
are many widely different ways in which it may be greatly in- 
creased. Thus, a gas becomes a conductor if it be highly heated, 
or if it be mixed with gas drawn from the vicinity of glowing 
metals or of the electric arc, or if an electric spark be passed 
through it, or if it be exposed to any of the cathode, Lenard, 
Becquerel or X-rays described above, or if it be exposed to ultra- 
violet light, etc., etc. This increase in conductivity is best shown 
by means of a gold leaf electroscope. So long as the surrounding 
air remains in its normal state, the leaves, if charged, remain 
diverging, or if they fall together, do so very slowly. If, how- 
ever, the air be rendered conductive, as for example by holding 



HIGH POTENTIAL. 



551 



within a foot or so of the leaves a minute quantity of a radium 
salt, the leaves collapse at once. The following experiment 
illustrates the production of conductivity by the X-rays. In 
Fig. 364, A is an X-ray tube enclosed in a thick box of lead with 
a small aperture in the top through which the rays may emerge. 
Immediately above this opening there is an inverted funnel F 



c O 




Fig. 364. 

which communicates through a glass tube with the jar B in which 
the electroscope is suspended. The X-rays render the air 
through which they pass conductive, for if suction be applied to 
the tube C so as to draw the air within F over into the jar B, the 
leaves collapse as soon as this air enters the jar. 

681. Ionization of Gases. — In the preceding paragraph we saw 
how the air within the funnel F (Fig. 364) was rendered conduc- 
tive by the action of the X-rays and how it retained this con- 
ductivity after it had been drawn over into the jar B. If, however, 
there be placed in the tube between F and B a plug of glass wool, 
the air from F after passing through this plug will be found to 
have lost its conductivity. The same thing happens if this air 
be drawn through a metal tube of fine bore, or if it be caused to 
bubble through water. Since, therefore, the conductivity of 
the air may be thus removed by filtration, it is but natural to 
ascribe it to the presence of material particles. Furthermore, the 
conductivity is removed if the air be passed between two parallel 
metal plates between which a strong electric field is maintained. 
These material particles must therefore carry electric charges. 
and since the air as a whole shows no sign of a charge, there must 
be an equal amount of positive and negative charges present. 
The theory was therefore advanced by Thomson that the con- 



552 ELEMENTS OF ELECTRICITY. 

ductivity of a gas is due to the presence of particles or part mole- 
cules, called ions, some positively and others negatively charged. 
These negatively-charged particles are found to be identical with 
the corpuscles of the cathode ray. The production of these ions, 
or ionization, is brought about by any of the agents mentioned 
in the preceding paragraph. The explanation advanced is that 
the electrons associated with these various agencies are moving 
with such velocity that when they come into collision with the 
molecules of the gas through which they pass, they break these 
molecules up into other ions. 

682. Investigation of Electrons. — From the time that the 
theory was advanced that the cathode rays consisted of charged 
electrons moving with high velocity, efforts were directed to 
determine the mass of these electrons, the charge which they 
carry and the velocity with which they move. In the solution 
of this problem the work of J. J. Thomson has been especially 
noteworthy. We can do no more than give a bare outline of his 
methods. 

His first step was to determine the relation between these 
three quantities, and this he did as follows. In the neck of the 
two-chambered Crookes tube shown in Fig. 365, B and D are two 



thick metal diaphragms pierced by an opening about a millimeter 
in width. The diaphragm B forms a part of the anode A. The 
rays from the cathode C pass in a narrow line through the slits 
in B and D and produce a small luminous spot at E on the far 
side of the other end of the tube. 

Let the mass of each electron be m grams, its velocity be v 
centimeters per second and its charge q electro-magnetic absolute 
units (Par. 536). Each moving electron is equivalent to a cur- 
rent whose strength is vq absolute units. If the tube be placed in 
and zt right angles to a uniform magnetic field of intensity H, 
each electron will be acted upon by a force vqH at right angles 



HIGH POTENTIAL. 553 

to its. path (Par. 356). Now it is shown in mechanics that if a 
body moving with uniform velocity be acted upon by a constant 
force at right angles to its path, then the body will move upon the 
arc of a circle. The radius of this circle is given by the expression 

r = -j~>f being the force at right angles to the path. The deflected 

electrons therefore move upon an arc whose radius is 

mv 2 mv 




vqH qH 

If the positive direction of the field be from front to rear, the 
rays DE will be curved downward to DF. DE, the tangent 
to the arc, and EF are measured, 
whence the radius of the circle is de- 
termined thus: 

The triangles CDE and DFE (Fig. 
366) being similar 

EF :DE ::DE :CE 

whence 

EF :DE ::DE :2r + EF 

DE 2 
whence 2 r = w - EF Fig 366 

The intensity of the field being measured, we have H and r, and 

771V 

the value of — becomes known. 
Q 

683. Velocity of Electrons. — The velocity v of the moving 
electrons was determined by Thomson as follows. Coils were 
placed in front and rear of the tube shown in Fig. 365 and a uni- 
form transverse magnetic field H established. If the positive 
direction of this field was from front to rear, the rays were deflected 
downward by a force vqH. 

The parallel metal plates P and N were connected to the ter- 
minals of the battery, thus establishing in the tube a vertical 
electric field F. If the plate P were positively charged, the rays 
would be deflected upward with a force Fq (Par. 674). By vary- 
ing either field (generally the magnetic field) they could be so 
adjusted that the tendency of one to bend the rays down was 



554 ELEMENTS OF ELECTRICITY. 

exactly balanced by the tendency of the other to bend the rays 
upward. At the instant 

vqH = Fq 

whence v = ~H 

and knowing F and H, the 
velocity v becomes known. This velocity, when the tube is highly 
exhausted, is about one-tenth of the velocity of light, and is in- 
dependent of the nature of the gas within the tube. 

By inserting this value of v in the expression deduced in the 
preceding paragraph we obtain the value of m/q, or the ratio of 
the mass of the electron to the charge which it carries. More 
frequently, the reciprocal of this ratio, or the ratio of q/m is given. 
According to the latest determinations it is 1.7 X 10 7 . It can be 
shown that in ordinary electrolysis the ratio of q/m for the hy- 
drogen atom is about 10 4 . 

684. Mass of Electron.— Having thus found the value of q/m 9 
if either one of these quantities be separately obtained the value 
of the other follows at once. The charge q is the one usually 
determined directly. The actual process involves many steps 
into which we can not go in detail. It is based upon the following 
principles. If a volume of saturated vapor be suddenly expanded 
its temperature falls and there is a tendency for condensation to 
ensue. If in such supersaturated space microscopic particles of 
dust be introduced, a fog is produced at once, the particles of dust 
facilitating condensation by serving as nuclei upon which the 
drops form. Now, if a closed vessel with an aluminum cover be 
exposed to certain radiations, such as those from radium salts, 
or to X-rays, electrons are produced in the gas within the vessel. 
These electrons act just like the dust in that they serve as nuclei 
for drops and in a supersaturated space cause a fog to form at 
once. These drops of mist are very minute but may be seen 
through a glass and by suitable observations the velocity with 
which they slowly settle can be determined. Knowing this veloc- 
ity and the density of the gas within the vessel, by the applica- 
tion of known formulae the size, and hence the mass, of the drops 
can be calculated. The vapor within the vessel contains both 
positive and negative ions but it has been found that if the ex- 
pansion is not greater than one-quarter of the original volume 



HIGH POTENTIAL. 555 

that only the negative ions serve as nuclei and are carried down. 
Each slowly-falling drop therefore has an electron as a nucleus. 
The charge carried by this electron has been determined in 
several ways. If the drop falls between two horizontal parallel 
metal plates, the lower plate can be given a negative charge so 
that its repulsion will counterbalance the force of gravity on the 
drop, or may drive it upward. By measuring the upward velocity, 
the force exerted upon it can be found, and hence the charge which 
it carries. 

Within the limits of experimental error, this charge is found to 
be the same as the charge carried by the hydrogen atom in ordi- 
nary electrolysis. Since we saw in the preceding paragraph that 
the ratio of q to m for the electron is 1.7 X 10 7 , and for the hy- 
drogen atom is 10 4 , and since q is shown to be the same in the two 
cases, the mass of the electron is 1700 times less than that of the 
hydrogen atom. On the other hand, the mass of the positive ions 
is found to agree with the mass of the corresponding atoms. 

685. Nature of Electrons. — Upon the nature of the negative 
ions or electrons, scientists are not entirely agreed. From what- 
ever substance produced, they appear to have the same mass. 
Some therefore maintain that they are the true atoms of a uni- 
versal single matter and that the fact that the weights of the 
majority of the ordinary chemical atoms may be expressed in 
whole numbers is simply an expression of a law of multiples 
which would follow from these atoms being composed of definite 
numbers of electrons. It would seem therefore that we had 
confirmed the belief of the alchemists that all matter was composed 
of a single and ultimate element. 

On the other hand, a few deny that they are matter and claim 
that they are portions of ether in rapid movement. 

Whatever be the nature of the electrons themselves, it is quite 
certain that the charges which they carry are electric atoms in the 
sense that they are all the same and that no smaller charge has 
yet been obtained. The atomic character of these electrons has 
already been mentioned (Par. 280). 



556 



ELEMENTS OF ELECTRICITY. 



CHAPTER 47. 



ELECTRIC OSCILLATIONS. 

686. Henry's Theory of Oscillatory Discharge of Leyden Jar. — 

Seventy-five years ago the identity of static and voltaic electricity 
was not regarded as proven. It had just been discovered that a 
voltaic current sent through a coil wrapped about a steel bar 
converted the bar into a magnet. It occurred to investigators 
that this fact afforded a means of making the desired proof. A 

steel needle was placed in a coil, one 
end of which was connected to the 
outer coating of a Leyden jar (Fig. 
367), the other end terminating in a 
knob near the knob which communi- 
cated with the inner lining. When a 
spark was caused to pass between the 
knobs, this charge passed through the 
coil and if it were of the same nature 
as voltaic electricity it should mag- 
netize the needle. When this was done 
it was found, according to expectation, 
that the needle became magnetized. 
1§ ' However, when these investigations 

were continued it was noted that although the charge was sent 
through the coil always in the same direction, the polarity of the 
resulting magnets varied in an anomalous manner so that it was 
not possible to predict which end of the needle would be the north 
pole. In seeking to explain this, Henry in 1842 advanced the 
theory that the discharge of a Leyden jar, although appearing to 
our senses as a single spark, was in reality an oscillation of a 
current back and forth, and the polarity of the needle depended 
therefore upon the direction of the last oscillation. 

687. Thomson's Mathematical Proof of Oscillation. — Some ten 
years after Henry announced his theory, Sir William Thomson 
(Lord Kelvin) advanced a mathematical proof of its correctness. 
His deduction may be shown as follows: 




HIGH POTENTIAL. 557 

Suppose that a Leyden jar of capacity C is discharged through 
a conductor of resistance R and of inductance L, and suppose 
that at any given instant it contains a charge q. The energy of 
the electro-static field of the jar at this instant is (Par. 97) 

|(«7C) 

This energy is being dissipated in two ways; (a) in establishing 
an electro-magnetic field about the conductor and (b) in heating 
this conductor. 

If the instantaneous value of the current be I, the energy of 
the electro-magnetic field is (Par. 359) ~ IN, or since N = LI 
(Par. 434) 

\PL 

Since I = — -~, the rate at which the charge is diminishing, 

this may be written 

'dq 



mi 



The rate at which energy is being lost by the jar is equal to the 
rate at which energy is being gained by the field plus the rate at 
which it is being expended in heating the circuit. 

The rate at which energy is being lost by the jar is 

_ q dq 
77 ' dt 

The rate at which it is being gained by the field is 

T dq d 2 q 
dt 'W 

The rate at which it is being dissipated in heat is 
PRt r2D fdq^ 



?-"■©« 



whence 



whence 



C ' dt 



_ T dq d' 2 q fdqY 

~ L dt 'dc> + h [dt) 



<Pq R dq q 
dt 2 ~^ L ' dt^ LC~~" 



558 ELEMENTS OF ELECTRICITY. 

A differential equation of this form may be solved by substi- 
tuting e mt for q (Murray, Differential Equations, Par. 50). 
Making this substitution we have 



m-e mt + £ me mt + Xi e mt = 



whence 



m i m *+z m +m) = 



which is satisfied when 
or when 



o i R i 1 A 



m= -2L ± 



R . i R- 1 



SIU>-LC ® 



The values of m are real when the quantity under the radical 
is positive, that is, when R- > 4 L / C. Designating these values 
of m by — m 1 and — m 2 (since they are both negative), the cor- 
responding value of q is 



— niit I h*~ m -2t 



q = ae~ nht + b 



a and b being constants. 
If t be made equal to zero, we have 

q = a + b 

q in this case being the value of 
the charge in the jar just before the discharge began. As t in- 
creases, corresponding to subsequent time, the value of q gets 
steadily smaller (since the exponents of e are negative), that is, 
the charge dwindles away without fluctuations or change of sign. 
The discharge is therefore unidirectional. 

If, however, R 2 is less than 4L/ C, the values of m in (I) above 
are imaginary. In this case we may proceed as follows: 

The expression for m is written 



m 



R J 1 R 



±\77j-m( v -v 



L^y LC 4L 



R 

and placing a = — j , 

i r>2 

\/ Y~r ~ Z72 an d * ™ ^ — 1> the- corresponding roots may 

be written 

m l = a + (3i 
m 2 = a — fii 



HIGH POTENTIAL 559 

whence as above 

which can be put in the form (Murray, Par. 52) 

q =e at (A cos pt + B sin/30 

If the exp ression within the parentheses be multiplied and 
divided by VA 2 + B 2 , we have 

A B 



VA ^ B {vWT3' C0 ^ t + 



sin /ft 



V'A 2 + B 2 VA 2 + 5 s 

which may be written 

A i (sin 4> cos /ft + cos <j> sin /ft) 

which is equal to 

Ai sin (pt + 0) 

and substituting above 

q = A-e at sin (pt + </>) 

In this expression, t being the only variable, we see that q varies 
harmonically, in other words, the discharge is oscillatory, although, 
since a is negative, the oscillations gradually die out. 

Since pt is the variable angle and t is time, p is angular velocity 
and the periodic time of an oscillation is 2ir/p. Substituting the 
value of p from above 

2tt 4ttLC 



/JL_ R^ VALC-R 2 K 2 
V LC 4L 2 

If R be very small, which is usually the case, R 2 C 2 may be 
neglected and this last expression reduces to 

r = 2tt VLC 

whence, the periodic time 
increases with an increase in L, the inductance, or in C, the 
capacity. 

688. Feddersen's Experiment with Revolving Mirror. — In 1859 
Feddersen by a simple experiment proved the correctness of 
Henry's theory and of Thomson's deductions. The principle he 
employed will be understood from the following. In Fig. 368, G 
is the spark gap of a Leyden jar, M is a mirror mounted upon an 
axis about which it is capable of rapid rotation, and P is a photo- 



560 



ELEMENTS OF ELECTRICITY. 



graphic plate. If while the mirror is rotating a spark be passed 
across the gap G, the beam of light from this spark will fall upon 
the mirror and will be reflected. Owing to the movement of M, 
this reflected beam will sweep like a brush across P and when the 
plate is developed and printed the path will be revealed as a band 
of light. Examination will show along the edges of this band a 
series of bright beads, those on one side being opposite the gaps 






Fig. 368. 

between those on the other and showing that the brightest point 
of the spark alternated between the knobs, in other words, the 
spark passed back and forth. Knowing the rate of rotation of 
the mirror, the time of oscillation of the spark may be determined 
with accuracy, even though this time is less than a millionth of a 
second. 

689. Explanation of Oscillation. — An explanation of this oscil- 
latory discharge is afforded by what we have already learned of 
inductance. Suppose a charge to be given to the jar and to be 
gradually increased until the discharge takes place. As the charge 
passes from the inner to the outer coating of the jar, it is a true 
current and the inductance of the circuit causes it to continue to 
flow beyond the point when the jar is completely discharged, in 
other words, the outer coating receives an excess charge. This 
then flows back in the opposite direction and, for the reason given 
above, the inner coating now acquires an excess charge, and so on. 
These oscillations do not continue indefinitely because at each one 
a portion of the energy is spent in heating the circuit and, as we 



HIGH POTENTIAL 561 

shall see shortly, another portion is radiated off into space. The 
total number therefore may not exceed ten or twelve. 

Reflection will show that before the discharge takes place the 
energy of the field is electro-static, that is, the field is composed of 
tubes of force (Par. 62), but that during the discharge this energy 
is electro-magnetic, the conductor being surrounded by circular 
lines of force. At the end of the discharge the magnetic lines dis- 
appear and the tubes of force reappear, but reversed in direction. 
As the return oscillation begins, these tubes again give way to 
magnetic lines of force, which in turn are in reverse direction from 
the first set, and so on. 

690. Maxwell's Electro-Magnetic Theory.— In 1865 Maxwell 
published a mathematical analysis of the effects produced in the 
surrounding medium by an oscillatory discharge. As bases for 
his discussion he took the facts (a) that a current flowing in a con- 
ductor produces about the conductor a magnetic field, (b) that if 
a magnetic field about a conductor be varied, an E. M. F. is in- 
duced in the conductor, (c) that the electric force exerted in the 
space about a charge varies inversely with the dielectric capacity 
and (d) that the magnetic field about a current varies with the 
permeability of the dielectric. To these he added the displace- 
ment assumption which is that when, for example, a charge flows 
into a condenser, an equal quantity of electricity moves in the 
dielectric between the plates, but that this movement takes place 
within the molecules of the dielectric and not from one molecule 
to another. The effect is as if in each molecule a positive charge 
had moved to one end, a negative charge to the other, and the 
positive charged ends all pointed in the same direction, that is, 
away from the positive plate of the condenser. The so-called 
displacement currents, just as any other current, produce about 
them a magnetic field. See Par. 55. 

As a result of his discussion he showed that these oscillations 
give rise to electric waves in the surrounding space, the wave 
front comprising electric displacements and magnetic forces at 
right angles to each other and both at right angles to the direction 
of propagation of the wave. He also showed that these waves 
moved with a velocity of thirty billion centimeters per second. 
Since light moves with the same velocity and is transmitted by 
the same agent, the ether, he concluded that light and electricity 
are identical and differ only in that the light waves are much the 



562 ELEMENTS OF ELECTRICITY. 

shorter. As corroborating this last conclusion, he showed that 
since electric waves can not be transmitted through conductors, 
these bodies should not transmit light waves. As a fact, the 
metals are all opaque to light. The same reasoning would show 
that a transparent solid is a non-conductor and such substances 
are the best insulators. It does not follow however that all opaque 
bodies are conductors, for many, such as porcelain, marble, etc., 
owe their opacity to irregular crystallization or mechanically 
included impurities. The purest form of crystallized marble, 
Iceland spar, is transparent. 

Maxwell's mathematical discussion can not be repeated here, 
but by following a similar line of reasoning we show in the three 
following paragraphs how he arrived at one of his conclusions. 

691. Electric Elasticity. — The elasticity of a body is measured 
by the ratio of the stress exerted upon the body to the strain 
(elongation, compression, etc.) produced. Consider a sphere 
carrying a charge Q and surrounded by a concentric non-con- 
ducting shell of dielectric capacity K. Displacement will take 
place in the dielectric, a charge — Q being induced on the inner 
surface of the shell and a charge +Q being repelled to the outer 
surface. If the radius of the shell be r, the force per square centi- 
meter exerted upon the inner surface is « • -^ (Par. 90) . This is 

the stress to which the shell is exposed. The strain per square 
centimeter consists in driving the positive charge to the outer sur- 
face of the shell and is therefore -p— 2 - The electric elasticity, the 
ratio of the stress to the strain, is Air/ K. 

692. Electric Density. — In Par. 435 there was deduced an ex- 
pression for the inductance of a coil wrapped upon a circular core. 
If in this expression both I and L be absolute electro-magnetic 
units (instead of amperes and henrys), the expression becomes 

T AttW-T 2 

L = — ^ M 

in which n is the total number 
of turns, r is the radius of the coil and I is its length. 

In Par. 687 it was shown that the energy of an electro-magnetic 
field is \l 2 L. Substituting the above value of L and dividing 



HIGH POTENTIAL. 563 

by irr 2 l, the volume of the core, we obtain for the energy per cubic 
centimeter 



1 , (In\ 
2Mt) 



If for n/l, the number of turns per centimeter, we write N, 



this becomes l . ,, ,, N 



In mechanics it is shown that the energy of a mass m moving 
with a velocity v is ■= mv 2 . From analogy, therefore, 4^ is 
termed the electric mass per unit of volume. But mass per unit 
volume is density, therefore, 4 717* is the electric density of the 
field. 

693. Velocity of Propagation of Electric Wave. — If e be the 
elasticity of a medium and 8 be its density, the velocity with 
which waves are propagated through it is v — Ve/8. Substitut- 
ing the values of the electric elasticity and density given in the 
preceding paragraphs, we have for the velocity of propagation 

of electric waves 1 

v = —= 

VKijl 

This is the expression which we have already obtained in Par. 
548. This velocity, by many independent methods, has been 
shown to be thirty billion (3xl0 10 ) centimeters per second, or 
as already stated, the same as the velocity of light. 

694. Hertz's Confirmation of Maxwell's Theory. — During 
Maxwell's life time his theory made but moderate headway and 
he died before it had ever been experimentally proven. In 1887, 
twenty- two years after his theory had been announced, it re- 
ceived striking and abundant confirmation by a series of brilliant 
experiments performed by Hertz. The arrangement used in the 
first of these experiments is shown in Fig. 369 and consists of 
two parts which Hertz designated respectively as the oscillator 
and the resonator. The oscillator consisted of two sixteen-inch 
square zinc plates, A and B, placed two feet apart. A copper 
rod from each of these and upon their common axis terminated 
in polished knobs separated by a gap G of about one-quarter 
of an inch. These rods were connected as shown to the terminals 
of the secondary of an induction coil. When the coil was operated, 
series of sparks passed between the knobs. The resonator con- 
sisted of a copper wire bent into a circle with a narrow spark gap 



564 



ELEMENTS OF ELECTRICITY. 



between two knobs. It was found that to obtain the best results 
the dimensions of the resonator had to be adjusted, or it had to 
be ' 'tuned" to suit the particular oscillator used.- With the one 
described, the diameter of the resonator was about twenty- 
eight inches. 




-o- 




Fig. 369. 

With the coil in operation and sparks passing between the 
knobs of the oscillator, the resonator was held in various near-by 
positions. When placed, as shown in the figure, along the line 
GM passing through and perpendicular to the spark gap G, it 
was found that sparks were produced in the gap of the resonator 
whenever the axis of this gap was parallel to the spark gap of 
the oscillator. Thus sparks were produced when the resonator 
was held as at C but not when held as at D or at E. 

As thus carried out, this experiment does not conclusively 
show the existence of waves and might be considered a simple 
example of induction as explained in Par. 420. The demonstra- 
tion of the existence of waves was made as follows : The oscillator 
was placed so that its axis was parallel to and at some distance 
from the opposite wall of the room in which the experiments 
were carried out. This wall was covered with large sheets of 
zinc M. Since according to Maxwell's theory the metals are 
opaque to these waves, this zinc sheet should act towards them 
as a mirror. Now it is well known that when waves strike a 
surface normally and are reflected back along the same path, 
the phenomenon of interference occurs. Beginning at the re- 
flecting surface, at fixed points one-half of a wave length apart 



HIGH POTENTIAL. 565 

the advancing and returning waves are in opposition and com- 
plete interference results, while at points midway between these 
nodes the waves are in phase and the resulting amplitude is twice 
that of the advancing wave. With the resonator close to the 
zinc sheet M, no sparks are obtained, but moving from M towards 
G, a point is found where the intensity of the sparks in the reson- 
ator is a maximum. Continuing to move towards G, the sparks 
in the resonator again die out, then again rise to a maximum. 
These electro-magnetic radiations are therefore waves, the dis- 
tance between two successive points of maximum sparking or 
between two nodes of no sparking being one-half of the wave 
length. With the apparatus described above, the wave length 
was found to be about thirty-two feet. 

By the method just outlined, the wave length can be deter- 
mined. By photographing the spark seen in the revolving mirror, 
the periodic time of the oscillations can be measured. The re- 
ciprocal of this is the frequency, or number per second. The 
product of the wave length by the frequency gives the velocity 
with which the wave travels. The results entirely confirm the 
previous determinations of this velocity as 3xl0 10 centimeters 
per second. 

695. Further Experiments by Hertz. — With slight modifica- 
tions in his simple apparatus, Hertz succeeded in reproducing 
many of the characteristic experiments usually shown with light. 
Thus, by placing the spark gap of his oscillator at the focus of a 
reflector made by bending a sheet of zinc into a parabolic form, 
he was able to direct the waves so that they could be detected 
by a resonator placed at the focus of a corresponding reflector 
at a distance of over thirty yards. By using a huge prism of pitch, 
four feet on an edge, he was able to refract the beam from the 
parabolic reflector. Finally, he showed that these waves are 
polarized. By placing in the path of the beam from the reflector 
a screen made of a number of parallel wires strung on a wooden 
frame, he showed that the waves pass freely when the wires 
were perpendicular to the axis of the spark gap of the oscillator 
but were entirely cut off when these wires were turned so as to 
be parallel to this axis. 

696. Length of Electro- Magnetic Waves. — The length of the 
longest light waves is a little over .00007 of a centimeter, while 



566 ELEMENTS OF ELECTRICITY. 

we have seen above that that of the electro-magnetic waves 
produced by Hertz in his first experiment was thirty-two feet. 
Since the velocity of these waves is constant and is equal to the 
product of the wave length by the frequency, and since the 
frequency is the reciprocal of the periodic time, the wave length 
varies directly with the periodic time. In Par. 687 this was shown 
to be r = 2t vL C, therefore, by decreasing either the inductance 
or the capacity of the oscillator, the wave length may be shortened 
provided the condition for oscillatory discharge, R 2 < 4L/ C (Par. 
687) be maintained. Since all conductors have both inductance 
and capacity, Hertz found that he could do away with the zinc 
plates of his oscillator and substitute for them simple straight 
wires. Other investigators, by reducing the dimensions of the 
oscillator, have produced electro-magnetic waves whose length 
has been about two-tenths of a centimeter. 

697. Principle of Wireless Telegraphy. — Hertz showed by his 
experiments that there could be produced at will electric waves 
which travel through space with the velocity of light. He also 
showed that by suitably-arranged apparatus these waves could 
be detected at a distance from their point of origin. It was 
quickly realized that these two observations comprised the funda- 
mental principle of wireless telegraphy. Subsequent development 
has taken place along two lines : (a) the improving of the sending 
apparatus or oscillator so that a greater amount of energy could 
be thrown out in the form of waves, and (b) the perfecting of the 
receiving apparatus, increasing its sensitiveness so that the waves 
could be detected at greater and greater distances. Foremost 
among those engaged in these problems was Marconi who in 
1895 took out his first patents on methods of wireless telegraphy. 

In order to bring out clearly the object of the various parts 
of the modern apparatus, we shall describe the simpler forms 
and show why changes were found desirable. 

698. The Antenna. — The waves used in wireless telegraphy 
are produced by an oscillating current of high frequency. We 
have seen that under certain conditions the discharge of a con- 
denser is of this nature. Hertz's oscillator, described above, is 
a condenser used for this purpose. It was soon discovered that 
the zinc plates could be replaced by straight wires. It was 
next found that if these wires be placed vertically instead of 



HIGH POTENTIAL. 567 

horizontally, the greater part of the lower one could be dispensed 
with, the earth taking its place. To this vertical wire the name 
antenna is applied. 

It is easily understood that the distance to which signals can 
be sent varies with the amount of energy radiated. We have 
seen (Par. 97) that the energy given out by a condenser on 
discharge is 1/2. F 2 C, therefore, we should endeavor to increase 
C, the capacity of the antenna. Since capacity varies with the 
dimensions, one way would be to increase the height, but the 
difficulty and cost of erecting lofty supports soon limit attempts 
in this direction. Marconi at first proposed that the antenna be 
supported by kites or balloons, but this was found to be imprac- 
ticable for permanent installations. Another way is to increase 
the number of wires in the aerial, or upper portion of the antenna. 
The capacity of a single wire is considerable. Pierce states 
that a straight wire y& inch in diameter and 100 feet long has the 
same capacity as an isolated metallic disc 16 feet in diameter. 
If, however, more than one wire be used, owing to the mutual 
action of the like charges which they carry, the capacity is far 
from increasing in proportion to the number of wires, in fact, it 
increases more nearly as the square root of this number, that is, 
sixteen wires two feet apart have only four times the capacity of 
a single wire. 

There are numerous patterns of antennae but the most usual 
form now consists of one or more horizontal wires, supported by 
towers or masts, from which they are insulated, and connected 
by a vertical lead-in wire to the station below. 

699. The Transmitter. — The simplest form of sending ap- 
paratus or transmitter is represented diagrammatically in Fig. 
370. It will be seen that it is nothing more nor less than the 
induction coil as described and figured in paragraphs 438 and 439, 
the spark gap G being placed vertically and one of its wires pro- 
longed above into the antenna, the other below into the ground. 
It must also be noted that the aerial and the ground constitute 
an air condenser of small capacity shunted across the spark gap. 
Any difficulty in realizing this will be removed if we consider 
them to be curved over as shown by the dotted lines. 

When the key is closed a current flows through the primary and 
at each break of the interrupter the high induced E. M. F. in the 



568 



ELEMENTS OF ELECTRICITY. 



secondary charges the antenna-ground condenser until its voltage 
rises sufficiently to cause a spark to leap across the spark gap, 
when, if the resistance, inductance and capacity be so propor- 
tioned that R 2 is less than 4L/C (Par. 687), an oscillating current 
will surge back and forth in the antenna, producing the desired 
waves. This condenser can not discharge back through the 
secondary coil since the latter, consisting of many turns of wire 
upon an iron core, acts as a choke coil (Par. 621). 







Fig. 370. 



Before the spark leaps across, the resistance of the spark gap 
is high, but the passage of the spark produces ionization and 
reduces the resistance very materially. At each oscillation across 
the gap, a portion of the energy is spent in developing heat in the 
circuit and gap and another portion is radiated off in the waves 
produced, therefore, the energy is very quickly reduced to the 
point where the oscillations cease and the gap resistance is re- 
established. 

The arrangement just described has the advantage of sim- 
plicity but has a number of disadvantages, one being the position 
of the spark gap with its large resistance in the oscillatory circuit, 
but the most serious being lack of power. The power which it 
develops can not exceed that with which it is supplied by the 



HIGH POTENTIAL. 



569 



battery and induction coil and this restricts its use to relatively 
low-powered plants j not exceeding one kilowatt. 

700. Improved Form of Transmitter. — To overcome the ob- 
jections to the simple transmitter described above, the arrange- 
ment shown in Fig. 371 is used, the salient features being (a) the 




Fig. 371. 

use for the source of power of an alternator, A, and a step-up 
transformer instead of a battery and induction coil, (b) the 
insertion between the secondary of the transformer and the 
antenna of a circuit including inductance L\ and large capacity 
C, (c) the removal of the spark gap G from the antenna circuit to 
the intermediate circuit, and (d) the insertion of inductance L 2 
in the antenna circuit. There are thus really four circuits em- 
ployed. The first comprises the alternator, the primary of the 
transformer and the key by which signals are produced. The 
second contains the secondary of the transformer and the con- 
denser C. The third includes this same condenser, the inductance 
Li and the spark gap G. The fourth includes the antenna- 
ground condenser and the inductance L 2 . 

The alternator furnishes to the primary a 500 cycle current of 
110 to 220 volts, the secondary delivering 5,000 to 20,000 volts 
and thus charging the condenser C. 

The discharge of the condenser produces an oscillating current 
in the circuit CL x G y for which reason this is called the closed 
oscillatory circuit, the antenna sj^stem being the open, or radiating 
oscillatory circuit. 

Energy may be transferred from the closed oscillatory circuit 
to the antenna in two ways. First, the coil L 2 may be removed 



570 ELEMENTS OF ELECTRICITY. 

and the antenna and its ground wire connected directly to L lm 
In this case the arrangement is really an auto -transformer (Par. 
652), the two circuits are said to be direct coupled and the antenna 
directly excited. Second, the wiring shown in Fig. 371 is used. 
The circuits are now said to be inductively coupled and the antenna 
indirectly excited. It must be remembered, however, that the 
figure is diagrammatic and that the coils L x and L 2 are really 
placed coaxially, either in prolongation of each other, or differing 
in diameter and one inserted within the other. They thus con- 
stitute an air core oscillation transformer. Preference is given to 
the inductive coupling. 

701. Resonance. — The action of the secondary of the trans- 
former (Fig. 371) is to impress an alternating E. M. F. upon the 
closed oscillatory circuit. This will produce a current, the ex- 
pression for which is (Par. 630) 

E 



\R* + (2 tt/L 



27T/C 



and we have seen (Par. 631) that this current is a maximum when 
resonance is attained, or when 

2tt/L = - ] - 

27T/C 

or when 

1 



/ 



2tt VLC 



The energy in the closed oscillatory circuit is transferred to 
the open oscillatory or antenna circuit (Par. 700) and in order 
that the current in this latter may be a maximum, it, also, must 
be adjusted to the same frequency. If L\ and C\ are respectively 
the inductance and capacity in the closed oscillatory circuit, and 
if L 2 and C 2 be the same for the antenna circuit, then in order 
that the frequency in the two circuits should be the same, L 1 C 1 
should be equal to L 2 C 2 . The capacity C 2 of the antenna system 
is small, therefore, in order to attain the above condition, L 2 must 
be large, which is the reason for the use of the coil L 2 as shown 
in Fig. 371. 



HIGH POTENTIAL. 571 

We can determine when the antenna circuit is in resonance with 
the closed oscillatory circuit by inserting in the former a hot wire 
ammeter (Par. 463) and varying the inductance L 2 until a maxi- 
mum current is indicated by the instrument. 

702. Wave Lengths Used.— In Par. 687 it was shown that the 
periodic time of an oscillatory discharge is 

r = 2tt VLC 

The frequency is the reciprocal of this, or 

1 



/ 



2tt VLC 



The velocity of propagation of electro-magnetic waves is the 
same as that of light, or three hundred million, (300,000,000), 
meters per second, and is independent of the frequency. The 
length of a wave is therefore 

>-? 

or 

X = v X 2tt VLC 

With a given transmitter we may therefore vary the length of 
the emitted waves by varying L, the inductance, or C, the capacity 
(Par. 696). However, in such systems, the power is relatively 
large and it is not desirable to vary L or C greatly. Such stations 
are therefore designed to produce waves of a particular length. 
Since a moderate change in wave length is sometimes required, 
and since, as we have shown above, we may increase this length 
by increasing L, the inductance, the antenna is designed for the 
minimum length to be sent out and is arranged, as shown in 
Fig. 371, so that additional inductance may be added by attach- 
ing the movable clip at the foot of the aerial to various turns of 
the coil L 2 . 

On the other hand, receiving stations deal with very minute 
power and the above factors can be varied so as to receive a wide 
range of incoming waves. 

The U. S. Radio Laws, (which are liable to change at any time), 
require transmitting stations to use the following wave lengths; 



572 ELEMENTS OF ELECTRICITY. 

Amateurs below 200 meters frequency 1,500,000 

Ships 300 to 600 meters 1,000,000 down 

Navy 600 to 1200 meters 500,000 down 
High Power 

Stations above 1600 meters 187,500 down 

For long distance transmission, the long waves are found to be 
the best and some high power stations use wave lengths in excess 
of 10,000 meters. 

The wave length in an oscillating circuit may be determined by 
a wave meter, an instrument which when placed near such a circuit 
and adjusted to resonance with it, indicates directly from a grad- 
uated scale the length of the wave. 

703. Two Kinds of Waves. — The waves used in wireless are 
of two kinds, damped and undamped. Damped waves are pro- 
duced by the spark apparatus such as we have described. They 
start with the discharge of the condenser, quickly attain maximum 
amplitude, then dwindle away rapidly and cease after, say, six 
to ten oscillations, to be resumed at the next discharge, and so on. 
With a 500 cycle alternator as a source of power and with the 
spark gap adjusted to give one discharge per alternation, the 
spark frequency is 1000. This number of sparks per second may 
seem to place the oscillations in the undamped class, however, 
the frequency of the condenser oscillations may exceed 1,000,000, 
and in such case the duration of the entire train of ten oscillations 
is only one one-hundred -thousandth of a second whereas the 
interval between sparks is one-thousandth of a second, therefore, 
for ninety-nine hundredths of this interval there are no oscilla- 
tions. See A, Fig. 373. 

Undamped waves are produced, among other ways, by very 
high frequency alternators of special design. They are analogous 
to the vibrations of a violin string when emitting a sustained note. 

704. Detection of Electro-Magnetic Waves. — We have seen 
how electro-magnetic waves are produced and how they radiate 
in all directions from the source and travel with the velocity of 
light. We shall now see how they may be detected. 

When these waves encounter a conductor, they produce in it 
an alternating E. M. F. If, therefore, there be erected an an- 
tenna similar to those used in transmitters, and if its resistance, 



HIGH POTENTIAL. 



573 



capacity and inductance be properly adjusted, an oscillatory 
current will be produced in it by such waves. It will be realized 
that since the energy radiated falls off inversely as the square of 
the distance from the origin and that since every tower, church 
spire, tree, pole, guy wire, etc., over which these waves pass acts 
as an antenna and absorbs a portion of this energy, that the 
amount reaching the antenna is exceedingly minute and the 
currents correspondingly small. In order that the currents pro- 
duced in them may have their maximum value, receiving circuits 
should be tuned to resonance with the particular station from 
which waves are being received, but even then these currents are 
far smaller than can be measured by the usual instruments. 

One of the earlier pieces of apparatus which enabled wireless 
signals to be received was Branley's coherer, now obsolete. It 
acted in an analogous manner to the relay in the Morse system 
(Par. 412) and turned the current from an auxiliary battery in 
upon a sounder which emitted the usual dots and dashes. The 
coherer has given way to far more sensitive pieces of apparatus, 
two of which we shall describe, and the relay has been displaced 
by sensitive telephone receivers. Pierce states that while it 
requires about 1/200 of a volt to operate a relay, a 540 cycle 
alternating E. M. F. of 8 millionths of a volt will produce an 
audible sound in the telephone. 

705. Receiving Set.— The usual form of receiving set, shown 
in Fig. 372, is similar to the transmitting set as described in Par. 




Fig. 372. 

700 but consists of three circuits, an open oscillatory circuit, a 
closed oscillatory circuit and a telephone circuit. 



574 



ELEMENTS OF ELECTRICITY. 



The open oscillatory circuit consists of the antenna, (the same 
one used by the transmitter), which includes a variable induc- 
tance I#i. In order to pick out an incoming wave and to exclude 
others, the antenna circuit must be tuned to resonance with the 
particular one. We have seen (Par. 702) that the wave length 
varies directly with VLC, therefore, we may tune by varying L 
or C. The clip contact by which the inductance L 1 is varied is 
usually shifted not less than one complete turn of the coil and 
therefore very fine adjustments can not be made. To remedy 
this, a variable condenser C Li (an air condenser whose capacity 
may be varied through all intermediate values by shifting one 
set of plates relatively to the other), may be connected in parallel 
with the antenna. Condensers in parallel add their capacities, 
therefore, to tune for long waves, this condenser is thrown in by 
closing its switch S. On the other hand, the capacity of con- 
densers connected in series is the reciprocal of the sum of the 
reciprocals of the several capacities, or is less than that of the 
least, so that to tune for very short waves there is sometimes 
used another variable condenser C s connected in series with the 
antenna and thrown in when needed by opening its switch S. 

The closed oscillatory circuit includes a variable inductance 
and a variable condenser and is tuned to resonance with the 
antenna circuit. 

The telephone circuit includes the detector D, described below, 
and the telephone head set T. 




SECOND 



V- 



lAA/w 



i\f\ 



j i/\/> 



Fig. 373. 



706. Crystal Detectors. — In 1896 General H. H. C. Dunwoody, 
(Class of 1866, U. S. M. A.), discovered that a crystal of car- 
borundum inserted in an alternating current circuit possessed 
the remarkable property of permitting the current to pass in one 



HIGH POTENTIAL. 



575 






direction but almost entirely suppressed it in the opposite direc- 
tion. Many other crystalline substances, such as the sulphides 
of lead, of molybdenum, of copper, the oxide ot zinc, silicon, etc., 
have since been found to act in this way and for this reason are 
often called crystal rectifiers. 

To explain their use, suppose A, Fig. 373, to represent the 
oscillations produced in a receiving circuit by the waves from a 
distant station. These can not affect the telephones because the 
metal diaphragms could never respond to vibrations of this high 
frequency, and even if they could respond, the frequency is far 
beyond that which the human ear can detect. The frequency 
of a high soprano voice is only about 1300. Now suppose a 
crystal detector to be placed as shown at D in Fig. 372. From 
what we have shown above, the oscillating current is now made 
practically unidirectional as shown in B, Fig. 373. The first 
impulse flowing through the telephone coil pulls the diaphragm. 
Before the latter has had time to spring back, it is given a second 
pull, and so on as long as the oscillations continue. The result 
is as if the diaphragm had been given a continuous pull by a 
current as represented in C, Fig. 373. It therefore vibrates 1000 
times per second and emits a clear musical note. Dots and dashes 
are determined by the length of time that the key at the trans- 
mitting station is held down. 

707. The Two-Electrode Vacuum Tube. — A still more sensi- 
tive and efficient form of detector now used is the vacuum tube, 
also called the audion, pliotron, etc. To explain this; Fig. 374 
represents a vacuous glass globe 
in which there is a metallic fil- 
ament F and a metallic plate P, 
connected as shown to the bat- 
teries A and B which are faced 
in opposite directions. Under 
these conditions, there is no cur- 
rent, but if the key K be closed, 
throwing the battery A on the fil- 
ament F, a current will flow at 
once through the circuit BPFB. 

When the filament F is heated by the battery A, it throws off 
electrons into the surrounding space, the number so emitted being 




Fig. 374. 



576 



ELEMENTS OF ELECTRICITY, 



a direct function of the temperature of F. P being made positive 
by the battery B, the electrons from F, all negatively charged, 
move towards P, thus establishing an electron flow in the direc- 
tion FP, or, (Par. 217), a current in the direction PF, called the 
plate current. An increase in the potential of P increases the 
current to a certain point, after which it remains constant. This 
is because the heated filament kept at a constant temperature 
emits electrons at a constant rate and when these are moved away 
as fast as they are produced, the current is a maximum. If the 
filament be heated to a higher temperature, it throws off electrons 
more rapidly and the current rises to a new maximum. 

708. The Three-Electrode Vacuum Tube. — Returning to the 
tube shown in Fig. 374, let us insert between F and P, as shown in 
Fig. 375, a metal plate G pierced with many slits and resembling 




H 




Z 




UJ 




(C 




&: 




=> 




o 




ul 




h- 




< 




—i 




Q- 










': 



-3 VOLT 5 



Fig. 375. 



3RITJ 

Fig. 376. 



+3 VOLTS 

POTENTIAL 



a grid iron, (and hence called the grid), and suppose that its po- 
tential with respect to F may be varied. If G be charged nega- 
tively it will repel the electrons coming from F, thereby dimin- 
ishing the plate current. On the other hand, if it be charged 
positively, it will aid the flow of electrons towards P, thus in- 
creasing the plate current. If we apply various potentials, 
positive and negative, to the grid and note the corresponding 
plate currents, it will be seen that for equal positive and negative 
variations of the grid potential, the variations in the plate current 
are by no means equal. Thus, Fig. 376 shows that when the grid 
potential is increased from to + 3 volts, the increase in the 
plate current is several times greater than the decrease produced 
when the potential is lowered from to — 3 volts. 



HIGH POTENTIAL. 



576a 



709. The Vacuum Tube as a Detector. — Fig. 377 represents 
diagrammatically a receiving set entirely similar to the one shown 
in Fig. 372 except that the vacuum tube is used in place of the 
crystal detector. Oscillating impulses coming in to the grid from 




j<L 




Fig. 377. 

L 2 alternately increase and diminish the potential of the grid, and, 
from what has been shown above, vary the current sent through 
the tube and telephone by the battery B. But, we have also seen 
that these variations are asymmetrical and that the average 
current through the telephone in one direction is greater than 
that in the opposite. The effect, therefore, is very similar to 
that of the crystal rectifier (Par. 706), the diaphragm of the 
telephone receiver is pulled in one direction by each wave train 
and the receiver emits a musical note. 



INDEX. 



577 



INDEX. 



References are to Paragraphs. 



Absolute measurement of current, 
374, 546 

of resistance, 542, 546 
Absolute temperature, 256 
Absolute unit of current, 355, 536, 546 

of E. M. F., 426, 537 

of electric power, 496 

of resistance, 427, 546 

of self-induction, 433 
Absolute zero of temperature, 289 
Accumulator, 237 

chloride, 241 

reactions, 244 
Acheson, 488 
Actinium, 679 

Adaptation of generator to work, 582 
Adjustment of mariner's compass, 183 
Advantages of electro-magnet, 405 

of multipolar machines, 574, 639 

of Edison battery, 253 
Aerial, 698, 701, 702 
Aging of magnets, 167 
Air, dielectric strength of, 93 
Air condenser, 86, 87 
Alpha rays, 679 
Alternating current, 554, 606 

compared with direct, 656 

graphic representation of, 555, 618, 
627 

rectification of, 556, 653 

transformation of, 648 

value of, 612, 613 
Alternating current motors, 657 

classes of, 658 
Alternating E. M. F., graphic repre- 
sentation, 555, 618, 627 

composition of, 611 
Alternation, 608 
Alternator, compound, 638 

di-phase, 644 



Alternator, field excitation of, 637 

inductor, 640, 643 

polyphase, 640, 644, 645 

single phase, 640, 644 

tri-phase, 645, 646, 647 
Alternators, 636, 649 

classes of, 640 

usually multipolar, 639 

with revolving armatures, 641 

with revolving field, 642 
Aluminum, manufacture of, 489 
Amber, 12 

American telegraph system, 413 
Ammeter, 455, 457, 459, 467, 471, 472, 
474, 702 

classes, 462 

connection of, 457, 459 

millivoltmeter as, 474 

resistance of, 457, 459 

Weston, D. C, 467 
Ammeter shunt, 465, 466 
Amount of induced charge, 31 
Ampere, 181, 344, 345, 346, 360, 371 
Ampere defined, 228, 232, 307, 448, 

544, 546 
Amperes, virtual, 612 
Ampere turns, 388 
Analogues of electric potential, 70 
Analogy between cells and pumps, 338 
Angle of lag, 609 

of lead, 570, 60 
Anode, 220 
Antenna, 698 
Apparent power, 635 
Application of electrolysis, 233, 23-4, 

235 
Arago, 428 
Arc, electric, 485 

enclosed, 521 

flaming, 522 



578 



INDEX. 



Arc lamp, 515 

constant current, 520 

constant potential, 519 

magnetite, 523 
Arc lamp mechanism, requirements 

of, 517 
Arc lights, efficiency, 524 
Armature, 124, 560 
Armature core, 560, 565 
Armature reaction, 570, 587 
Armatures, classes of, 566 
Arrhenius, dissociation theory of, 268 
Artificial magnets, 109 
Astatic combination, 366, 368 
Atomic character of electricity, 280, 

685 
Attracted disc electrometer, 101, 102 
Attraction, electric, 15, 16, 17, 30 

magnetic, 112, 120 
mutual, 114 

takes place through intervening 
bodies, 113 
Auto-transformer, 652, 701 
Avogadro's law, 256 
Ayrton, 381, 445, 454 
Back E. M. F., 297, 593, 594, 595 
Balance, Coulomb's torsion, 52, 100, 

127, 132 
Ballasting coil, 508, 519, 527 
Ballistic galvanometer, 384 
Base, electrolysis of, 223 
Battery defined, 191 

De La Rive's floating, 370 

development of power in, 49 

lead, care of, 248 
objections to, 249 
troubles of, 247 

storage, charging, 245, 246, 415, 
582 
Bauxite, 489 
Becquerel rays, 679, 680 
Bell, electric, 410 
Bell telephone, 440 
Beta rays, 679 
Bichromate cell, 205 
Bifilar suspension, 127, 382 
Biot's experiment, 39 
Bipolar generator, 561 



Blow out, magnetic, 485 
Bolometer, 534 
Boys, Vernon, 534 
Branley, 704 
Bridge, meter, 325 

slide wire, 325 
Bridge, Wheatstone, arrangement of 
resistances, 315 

evolution in form, 316 

measurement of resistances by, 317, 
318, 319, 320, 321 

principle of, 313, 314 

resistances measured by, 324 

with reversible ratios, 322 
Brushes, 553, 560, 568 

shifting of, 570, 571, 598 
Brush holders, 568 
Bunsen's cell, 204 
Bus bars, 579 
Buzzer, 704 
C. G. S. system, 10 
Calcium carbide, manufacture of, 488 
Calculation of E. M. F. of generator, 
578 

of flux of magnetic circuit, 401 
Calibration of galvanometer, 454 
Calorie, 11, 478 
Canal rays, 676 
Candle power, 509 
Capacity, 79, 607, 625 

E. M. F. and current curves in case 
of, 627 

of plate condenser, 89 

of sphere, 80 

of spherical condenser, 88 

of wires, 699 

practical unit of, 95 

and resistance, 629 

inductance and resistance, 630 
Capacity, electric, 45, 79, 83, 88, 95 
Capacity, dielectric, 31, 90, 92 

determination of, 91 
Capacity reactance, 628 
Carbon, variation of resistance with 
pressure, 285 

with temperature, 289 
Carbons for arc lamps, 516 
Carbon filament, 505 



INDEX. 



579 



Carborundum, manufacture of, 488 

use as detector in wireless, 706 
Care of lead batteries, 248 
Cathode, 220 
Cathode rays, 671, 672, 680 

effect of electric field on, 674 

effect of magnetic field on, 673 
Cell, bichromate, 205 

Bunsen's, 204 

Clark's standard, 212 

conventional sign for, 214 

Daniell's, 206, 427, 544, 546 

defined, 201 

dry, 210 

Edison-Lalande, 208 

electrolytic, 220 

elements of, 193, 194 

gravity, 207 

Grove's, 203 

Leclanche, 209 

Plante, 240 

primary, 201 

secondary, 237, 238 

simple, 193 

chemical action in, 195 
dissociation theory applied to, 
279 

standard, need of, 211 

Weston's standard, 213 

voltaic, requirements of, 200 
Cells, 191 

analogy with pumps, 338 

classification of, 202 

E. M. F. of, 200 

great variety of, 201 

grouping of, 334 

in multiple, 339 

in parallel, 336, 337 

in series, 335, 337 

internal resistance of, 294 

reversibility of, 236 
Centimeter, 7 
Characteristic defined, 583 

external, 585 

internal, 585 

magnetization, 584 

of series generator, 585 

of shunt generator, 587 



Charge, bound, 33 

carried by corpuscle, 675 

confined to surface, 38, 39, 68 

distribution of, 40 

division of, 45 

electric, 18 

free, 33 

induced, amount of, 31 
distribution of, 29 

of storage battery, indications of, 
246 

on conductor, 37, 68 

on non-conductor, 36 

on surface exerts no force on in- 
terior point, 67 

residual, 87 

surface density of, 41, 65, 66 
Charges, induced, separation of, 32 

variation of electric force with, 54 
Charging Edison battery, 252 

storage battery, 245, 246, 582 
from A. C, 655, 656 
Charles' law, 256 
Chart, isoclinic, 173 

isodynamic, 174 

isogonic, 170 
Chemical action in simple cell, 195 
Chloride accumulator, 241 

reactions, 244 
Choke coil, 621, 622, 650 
Circlet of cups, Volta's, 191 
Circuit, no current unless complete, 
216 

divided, 293 

division of current in, 300 
Circular coil, field at center, 354 

field on axis of, 354 
Circular measure of wires, 296 
Circular mil, 296 
Clark's standard cell, 212 
Classes of A. C. motors, 658 

of alternators, 640 

of armatures, 566 

of D. C. motors, 598 

of electrical machines, 550 
Classification of ammeters and volt- 
meters, 462 

of cells, 202 



580 



INDEX, 



Clutch for arc lamps, 518 
Coercive force, 398 
Coherer, 704 

Coil, choke, 621, 622, 650 
induction, 438 

use of condenser with, 439 
resistance, 311 

rotating in magnetic field, 551 
Collector rings, 553 
Commercial unit of electric power, 
496 
of electric work, 496 
Commutation, 556, 571 
Commutation plane, 570 
Commutator, 556, 560, 567 
Commutator segments, 567 
Comparison of A. C. and D. C, 656 
Compass, mariner's, 182 

adjustment of, 183 
Composition of alternating E. M. F.s, 

611 
Compound alternator, 638 

generator, 563, 588 
Condenser, 83, 86, 94, 96 
energy of, 97 
in A. C. circuit, 626 
location of charge in, 87 
use with induction coil, 439 
work expended in charging, 96 
Condenser, plate, capacity of, 89 

spherical, capacity of, 88 
Conditions affecting wireless teleg- 
raphy, 707 
Conductance, 292 
Conductivity, 292 

of gases, 667, 680 
Conductor denned, 19 
Conductors and non-conductors, 19 

table of, 20 
Conductors carrying currents, force 
exerted between, 361, 362 
in parallel, resistance of, 293 
in series, resistance of, 286 
Connection of transformers, 651 
Consequent poles, 165 
Constant current arc lamp, 520 
Constant potential arc lamp, 519 
Contact series, Volta's, 187 



Contact theory, Volta's, 188 
Control of field of machines, 564 

of light, 513 

of speed of shunt motor, 600 
Controlling force, 146 

method of weakening, 366 
Conventional sign for cell, 214 
Converter, rotary, 653 

synchronous, 653 
Cooper-Hewitt, 527 
Copper, refining by electrolysis, 238 
Core of armature, 560, 565 

of solenoid, effect upon field, 390 
Core transformer, 649 
Corpuscles, 672, 681, 682, 685 

mass of, 684 

nature of charge carried by, 675 

velocity of, 683 
Cost of power from primary cells, 343 
Coulomb, 38, 42, 52, 53, 100, 123, 128, 

132 
Coulomb, the, 56, 228, 536 

defined, 228 
Coulomb's first law, 115, 123 

second law, 128, 133 

torsion balance, 52, 100, 127, 132 
Counter E. M. F., 297, 593 

in motor, 593, 594 

reading of voltmeter across, 595 
Coupled circuits, 700 
Coupling of generators, 581 
Critical frequency, 631 

resistance, 586 
Crookes, 671 
Crookes' dark space, 670 

tube, 670, 671, 672, 675, 676, 677, 
678, 682 
Cryolite, 489 
Crystal rectifiers, 706 
Cumming, 529 
Curie, 679 

Current, absolute unit of, 355, 356, 
536, 546 

alternating, value of, 612, 613 

direction of flow of, 217 

displacement, 690 

division in divided circuit, 300 

eddy, 428 



INDEX. 



581 



Current — Continued. 

electric, 215 

effects of, 215, 444 
mechanical production of, 423 
work done by, 476 

equality at every cross section, 229 

Foucault's, 429 

measurement of, by tangent gal- 
vanometer, 374 

none unless circuit complete, 216 

practical unit of, 228, 307, 448, 546 

production by rotating coil, 553 

rotation by magnetic pole, 351 

units of, 536 
Curves of magnetization, 394 
Cutting of lines of force, 424, 425 
Cycle, 608 

of magnetization, 398 
Cylinder machine, 48 
D. C. generator, essential parts, 560 
Darnell's cell, 206, 423, 427, 544, 546 
Damping, electrical, 379, 430, 467, 471 
D'Arsonval galvanometer, 378, 467 
Davy, 223, 270, 515 
Dead beat instruments, 379 
Declination, annual change in, 179 

diurnal change in, 178 

magnetic, 169, 177 

secular change in, 177 
Decomposition, chemical, 257 

of water, 218 
Deflection of needle, right hand rule 

for, 345 
De La Rive's floating battery, 370 
Delta connection, 646 
Density, electric, 692 
Depolarizers, 199 
Detector, crystal, 705 

electrolytic, 705 
Detectors in wireless telegraphy, 703, 

704, 705 
Detonator, 483 
Diagrams, electric, 5- 

of parallel series grouping, 342 

vector, 610 
Dial bridge, 323 
Diamagnetics, 122 
Diamagnetism, 122, 402 



Dielectric, 55 

Dielectric capacity, 31, 90, 92 

determination of, 91 
Dielectric coefficient, 90 
Dielectric strength, 93 
Dimensional formula of resistance, 
540 

formulae, 539, 547 
table of, 547 
Difference of potential, 69, 73 
Dip, magnetic, 171, 177 

secular change in, 177 
Di-phase alternator, 644 
Dipping needle, 172 
Direct coupling, 701 
Direct current compared with alter- 
nating, 656 

transformation of, 648 
Direct current motors, classes, 598 
Direction of electric field, 59, 61 

of field about wire carrying a cur- 
rent, 347, 348 

of flow of current, 217 

of rotation of motor, 604 
Discharge through high vacua, 670 

through moderate vacua, 668 
Discovery of Galvani, 185 
Displacement current, 690 
Dissociation, 257 

by heat, 258 

extensive scope of theory of elec- 
trolytic, 281 

theory applied to simple cell, 279 

theory of Arrhenius, 268 
Distance attained by wireless teleg- 
raphy, 707 
Distribution of induced charge, 29 
Divided circuit, 293 

division of current in, 300 

drop of potential in, 312 
Division of charge, 45 
Drop of potential, 298, 299 

in divided circuit, 312 

measurement of resistance by, 309, 
310 
Drum winding, plane development of, 
576 

star development of, 577 



582 



INDEX. 



Drum wound armature, 566, 575, 576, 

577 
Dry cell, 210 
Dunwoody, 706 
Dynamo, 550 
Dynamotor, 605 
Dyne, 11 

E. M. F., absolute unit of, 426, 537 
counter, 297, 593 
in motor, 593, 594 
power of motor proportional to, 

594 
reading of voltmeter across, 595 
depends on rate of cutting of lines 

of force, 425 
induced at make and break, 437 
measurement by voltmeter, 461 
of cells, 200 

measurement of, 329 
of generator, 578 
of rotating coil, 552 
power, 617 
produced by cutting lines of force, 

425 
reactive, 619 
thermo-electric, 528 
units of, 537 
E. M. F.s, alternating, composition 

of, 611 
Earth a magnet, 116 
Earth's magnetic poles, location of, 

168 
Earth's magnetism, theories of, 181 
Earth's poles misnamed, 117 
Eddy current, 428 
Edison, 504 

Edison-Lalande cell, 208 
Edison storage battery, 250 

advantages and disadvantages, 253 
charging, 252 
reactions, 251 
Effect of points, 42, 43 
Effects of electric current, 215, 444 
Efficiency of arc lights, 524 
of incandescent lamp, 512 
of mercury vapor lamp, 527 
of motors, 596 
of transformers, 649 



Elasticity, electric, 691 
Electric arc, 485 

attraction and repulsion explained; 
30 

laws of, 24 
bells, 410 

capacity, 45, 79, 83, 88, 95 
charge, 18 

cause of movement, 69 
current, 215 

effects of, 215 

magnetization by, 164 

mechanical production of, 423 

work done by, 476 
density, 692 
diagrams, 51 
elasticity, 691 
field, 57, 58, 59, 61, 65, 66 

effect on cathode rays, 674 

graphic representation of, 61 

intensity of, 58, 61 

unit, 58, 61 
force, 54, 55, 58, 75 

variation with charges, 54 

variation with intervening medi- 
um, 55, 58 
furnace, 486, 497, 490, 491 
fuze, 483 

heating of wires, 480, 481 
light, 503 

lines of force, 60, 61 
pendulum, 22 
potential, 70, 72, 73, 74, 75, 83 

analogues of, 70 

how measured, 72 
power, absolute unit of, 49 

commercial unit of, 496 

expression for, 494 

measurement of, 497, 498 

practical unit of, 496 
primer, 483 
repulsion, 22 
resonance, 63 
telegraph, 411 
waves, 690, 694 

length of, 696 

velocity of propagation, 693, 694 
welding, 484 



INDEX. 



583 



Electric whirl, 44 

wind, 42, 44, 48, 49, 50 
work, commercial unit of, 496 
Electrical effects used in measure- 
ments, 444, 445, 446 
energy, source of in cell, 192 
machines, 46, 47, 48, 49, 50 

classes of, 550 
transmission of power, 501, 502 
Electricity, atomic character of, 280, 
685 
origin of name, 12 
static, 14 
theories of, 27 
two kinds, 26 
unit quantity of, 56 
Electrification, all bodies susceptible 
of, 21 
by influence, 28 
resinous, 23 
two kinds of, 23 
vitreous, 23 
Electro-chemical classification of the 

elements, 225 
Electro-chemical effect standard for 
measurements, 448 
unsuited for commercial measure- 
ments, 451 
Electro-chemical equivalent defined, 

231 
Electro-chemical rectifier, 653 
Electro-dynamics, 360 
Electro-dynamometer, measurement 
of power by, 498 
Siemen's, 383 
Weber's, 382 
Electro-magnet, 403 
lifting weights by, 409 
rule for polarity, 404 
shape of, 407 
use of, 408 
value of, 405 
Electro-magnetic effect used in meas- 
urements, 452, 453 
Electro-magnetic field, energy ex- 
pended upon, 359 
inertia of, 418 



Electro-magnetic induction explained, 

419, 420 
Electro-magnetic inertia, 418 
Electro-magnetic theory of light, 548, 

690, 694 
Electro-magnetic intensity, 535 
Electro-magnetic units, primary, 538 
Electro-mechanics, 549 
Electro-static units, 535 
Electrode, 220 

Electrolysis, applications of, 233, 234, 
235 

Faraday's terminology of, 220 

of a base, 223 

of fused compound, 222 

of a salt, 224 

of water, 219 

substances subject to, 221 
Electrolyte, 193, 220 
Electrolytes and non-electrolytes, 275 
Electrolytes, measurement of resist- 
ance of, 327 
Electrolytic cell, 220 

detector of wireless, 705 
Electrolytic dissociation, extensive 

scope of theory, 281 
Electrolytic properties depend upon 

ionization, 276 
Electrometer, attracted disc, 101, 102 

quadrant, 103, 104 
Electrometers, principle of, 100 
Electro-motive force, 76, 77, 78 (see 
E. M. F.) 

practical unit of, 77 
Electrons, 280, 672, 685 
Electrophorus, 35 
Electroplating, 234 
Electropoion fluid, 205 
Electroscope, 25 

gold leaf, 34, 680 
Electrostatic measurements, 98 
Electrotyping, 235 

Elements, electro-chemical classifica- 
tion of, 225 

magnetic, 175 
variation of, r 176 

of a cell, 193, 194 

of a secondary cell, 238 



584 



IXDEX. 



Enclosed arc, 521 

Energy, electrical, source of in cell, 192 
expended upon an electro-magnetic 

field, 359 
loss due to hysteresis, 399 
of a condenser, 97 
Equality of current at every cross sec- 
tion of circuit, 229 
Equation, Helmholtz's, 436 
Equipotential surface, 71, 72 
Equivalent, electro-chemical denned, 

231 
Erg, 11 

Essential parts of D. C. generator, 560 
Ewing, 153, 359, 399 
E wing's theory of magnetism, 153, 359 
Exceptions to Van't HofE's generaliza- 
tion, 267 
Excitation of field magnets, 562 
Exciter, 637, 656 

Explanation of motion of motor, 591 
Expression for electric power, 494 
for inductance of coil, 435 
for permeability, 392 
External characteristic, 585 
Fables of ancients concerning mag- 
nets, 107 
Factor, power, 635 
Farad, 95 
Faraday, 31, 38, 55, 91, 122, 181, 220, 

226, 230, 416, 417 
Faraday dark space, 670 
Faraday's discovery of induction, 416, 
417 
first law, 226 
ring transformer, 431 
second law, 230 

terminology of electrolysis, 220 
Feddersen's experiment with revolv- 
ing mirror, 688 
Fessenden, 705 

Field at center of circular coil, 354 
electric, 57, 58, 59, 61, 65, 66 
direction of, 59, 61 
effect on cathode rays, 674 
graphic representation of, 61 
intensity of, 58 
near uniformly-charged plane, 66 



near uniformly-charged sphere, 65 
unit, 58 
Field, electro-magnetic, energy ex- 
pended upon, 359 
inertia of, 418 

intensity of, about a straight con- 
ductor, 353 
Field, magnetic, about a wire carrying 
a current, 346 
direction of, 347, 348 
defined, 134 
determination of strength of, 148, 

149, 150 
direction of, 135 
effect on cathode rays, 673 
effect on positive column, 669 
graphic representation of intensity 

of, 145 
intensity of, 136 
Field of electrical machines, 143, 561 
of generator, 561 

of solenoid, effect of material of core 
upon, 390 
variation with current, 389 
on axis of circular coil, 354 
on axis of solenoid, 387 
rotary, production of, 664 [147 

Fields, magnetic, comparison of, 146, 

compounding, 141 
Field coils, 561 
Field control, 564 
Field excitation of alternators, 673 
Field magnets, 561 

excitation of, 562, 673 
Filament, carbon, 505 
Flaming arc, 522 
Fleming, 292 

Flow of current, direction of, 217 
Fluoroscope, 678 
Flux, calculation of, 401 
law of maximum, 144 
magnetic, 142 
Focusing tube, 678 
Force, coercive, 398 
electric. 75 

variation with charges, 54 
variation with intervening me- 
dium, 55, 58 



INDEX. 



585 



Force, electric lines of, 60, 63, 64 
from unit charge, 63 

electromotive, 76, 77, 78 (see E. M. 
F.) 

exerted between conductors carry- 
ing currents, 361, 362 

exerted by field upon conductor 
carrying a current, 356 

exerted on internal point of charged 
body, 67 

magneto-motive, 400 

tubes of, 62 

unit of, 11 
Forces, magnetic, measurement of, 127 
Formula, dimensional, of resistance, 

540 
Formulae, dimensional, 539, 547 
Foucault, 429, 515 
Foucault's currents, 429 
Franklin, 27, 43, 86 
Franklin's fulminating pane, 86 

theory of electricity, 27 
Free charge, 33 

Free ions, demonstration of, 272 
Free magnetism, 142 
Frequency, 608 

critical, 631 
Frictional machines, 46, 47, 48 
Furnace, electric, 486, 487, 490, 491 

induction, 491 

Moissan's, 487 
Fuse, 306, 481 

Fused compound, electrolysis of, 222 
Fuze, electric, 483 
Galvani, 185 
Galvani's discovery, 185 
Galvanometer, ballistic, 384 

calibration of, 454 

D'Arsonval, 378 

denned, 372 

mirror, 377 

reflecting, 378 

sine, 376 

suspended coil, 378 

tangent, 373, 546 
Galvanometer constant, 374 
Galvanometer shunts, need of, 380 



Galvanoscope denned, 363 

increase of sensitiveness, 364 

methods of weakening controlling 
force of, 366 
Gambey, 428 
Gamma rays, 679 
Gases, conductivity of, 667, 680 

ionization of, 681 
Gaseous pressure, laws of variation of, 

256 
Gauges, wire, 295 
Gauss, 11, 64, 148 
Gauss' theorem, 64 
Geissler tube, 670 
Generator, adaptation to work, 582 

and motor identical, 590 

calculation of E. M. F., 578 

compound, 563, 588 

ring wound, 569 

series, 563, 582 

characteristic of, 585 

shunt wound, 563, 582 
characteristic of, 587 
Generators, 423, 550, 560, 561, 563 

classes of D. C., 563 

coupling of, 581 

used in wireless telegraphy, 701 
Gilbert, 12, 108, 110, 116, 117, 121, 

156, 158, 159, 168 
Gold leaf electroscope, 34, 680 
Gram, 8 

Gravity cell, 207 
Gray, Stephen, 19 
Grid, 239 

Grotthus' theory, 274 
Grouping, mesh, 646 

of cells, 334 

of incandescent lamps, 514 

of storage battery plates, 243 

star, 647 
Grove's cell, 203 
Haiiy's method, 366, 367 
Heat, dissociation by, 258 

effect on magnetization, 158 

unit of, 11, 478 
Heating effect, laws of, 477, 478 
Heating effect of current, localizing, 
482 



586 



INDEX. 



Heating, electric, of wires, 480, 481 

Hefner, the, 509 

Helmholtz, 280 

Helmholtz's equation, 436 

Henry, the, 433, 434 

Henry, Professor, 403, 686 

Henry's theory of oscillatory discharge 

of condenser, 686 
Hertz, 694, 695, 696, 697, 698 
Hertz's confirmation of Maxwell's 
theory, 694, 695 

oscillator, 694, 699 

resonator, 694 
High potential, 666 
High resistance, measurement of, 326 
Hopkinson, 392 
Holtz's influence machine, 50 
Horse power, 494 
Hot wire instruments, 463, 702 
Hysteresis, 396 

energy loss due to, 399 
Impedance, 620 
Incandescent lamp, 504 

control of light of, 513 

efficiency of, 512 

life of, 511 
Incandescent lamps, grouping of, 514 
Inclination, magnetic, 171 
Inclined coil instruments, 471 
Increase in number of coils of gener- 
ator, 558 
Increase in number of turns of coil of 

generator, 557 
Increase of sensitiveness of galvano- 

scopes, 364 
Indicating wattmeter, 499 
Indication of charge of storage bat- 
tery, 246 
Induced charge, amount of, 31 

distribution of, 29 
Induced charges, separation of, 32 
Induced E. M. F. at make and break, 
437 

rule for direction of, 421, 422 
Inductance, 434, 615, 619 

and resistance contrasted, 616 
effect of alternating E. M. F., 617 
in parallel, 624 



Inductance and resistance in series, 

623 
Inductance, resistance and capacity, 

630 
Inductance of coil, expression for, 435 
Induction, electro-static, 28, 30 
Induction, electro-magnetic, explained, 
419, 420 

Faraday's discovery of, 416, 417 

magnetic, takes place through space, 
119 

magnetization by, 118 

self, 432, 614 
measure of, 433 
Induction coil, 438 

use of condenser with, 439 
Induction furnace, 491 
Induction motor, 428, 662, 663, 664, 

665 
Inductive coupling, 701 
Inductive reactance, 619 
Inductor, 560, 569 
Inductor alternator, 640, 643 
Inertia, electro-magnetic, 418 
Influence, electrification by, 28 
Influence machines, 46, 49, 50 
Instruments, hot wire, 463 

inclined coil, 471 

moving iron, 464 
Integrating wattmeter, 500 
Intensity, magnetic, 174 

of electric field, 58, 61 

of field about a straight conductor, 
353 

of force between conductors carry- 
ing current, 362 
Internal characteristic, 585 
Internal resistance of cells, 294 

measurement of, 328 
International ohm, 291 
International volt, 212 
Interrupter, 410, 438 
Intrinsic magnetism, 142 
Inverse squares, experimental proof 
of law, 131, 132 

law of, 53 
Inversion, thermo-electric, 529 
Investigations of Volta, 186 



INDEX. 



587 



Ionization, 268 

electrolytic properties depend upon, 
276 

how it takes place, 270 

incomplete, 271 

of gases, 681 

why it takes place in solutions, 269 
Ions, 220, 681 

free, demonstration of, 272 

not from same molecule, 273 
Iron-clad magnet, 409 
Iron furnace, electric, 490 
Isoclinic chart and lines, 173 
Isodynamic chart and lines, 174 
Isogonic chart and lines, 170 
Jars, unit, 99 
Joint resistance, 293 
Joule, 477, 478 
Joule, the, 478 
Joule's law, 478, 479 
Kelvin, Lord, 102, 103, 377, 529, 531, 

687 
Kirchoff's laws, 303, 304 
Lag, angle of, 609 
Laminated magnets, 166 
Lamp, arc, 515 

constant current, 520 

constant potential, 519 

magnetite, 523 
Lamp, incandescent, 504 

control of light, 513 

efficiency of, 512 

life of, 511 

manufacture of, 506 
Lamp, mercury vapor, 527 

Nernst, 508 

tantalum, 507 

tungsten, 507, 512 
Lamps, incandescent, grouping of, 514 
Lamps, luminous vapor, 525, 526, 527 
Lap winding, 575 
Laplace, 353, 361 
Law, Avogadro's, 256 

Charles', 256 

Coulomb's second, 128, 133 

Faraday's first, 226 

Faraday's second, 230 

Joule's, 478, 479 



Law, Laplace's, 361 

Lenz's, 430 

Mariotte's, 256 
osmotic pressure follows, 264 

Maxwell's, 144, 371, 377, 467, 470, 
471, 591 

of bifilar suspensions, 127 

of inverse squares, 53 

experimental proof of, 131, 132 

of magnetic circuit, 400 

of maximum flux, 144 

of torsion, 52, 127 

Ohm's, 297, 299, 307, 427, 538 

sine, 147 

tangent, 146 
Laws, Kirchoff's, 303, 304 

of heating effect, 477, 478 

of resistance, 285, 286, 287, 288, 289 

of variation of gaseous pressure, 256 
Lead, angle of, 570, 609 
Lead batteries, care of, 248 

objections to, 249 

troubles of, 247 
Leclanche cell, 209 
Left hand rule for direction of motion 

of current, 352 
Lenard rays, 677, 680 
Length, standard of, 4 

unit of, 7 
Length of electric waves, 696 
Lenz's law, 430 
Leyden jar, 85, 86, 87, 103 

Feddersen's proof of oscillatory dis- 
charge, 688 

invention of, 84 

oscillatory discharge of, 686, 689 

Thomson's proof of oscillatory dis- 
charge, 687 
Lichtenberg's figures, 36 
Life of incandescent lamp, 511 
Light, electric, 503 
Lifting power of magnets, 124 
Lightning rod, 43 
Lines, isoclinic, 173 

isodynamic, 174 

isogonic, 170 
Lines of force, cutting of, 424, 425 

electric, 60, 61, 63, 64 



588 



INDEX. 



Lines of force, from unit charge, 63 

magnetic, 137 

method of mapping, 138, 139, 

141 
pass preferably through magnetic 

substances, 143 
properties of, 142, 143 
Local action, 196 

remedy for, 197 
Localizing heating effect of current, 

482 
Location of earth's magnetic poles, 

168 
Lodestones, 106, 159 
Lost volts, 305 

Luminous vapor lamps, 525, 526, 527 
Machines, electrical, 46, 47, 48, 49, 50 

classes of, 550 
Magnet, origin of name, 105 

the earth a, 116 

tractive power of, 406 

turning moment of, 149 
Magnets, aging of, 167 

artificial, 109 

fables of ancients relating to, 107 

laminated, 166 

lifting power of, 124 

most suitable metal for making, 160 

mutual action of, 115 

natural, 105 

principle of manufacture, 161 

strength of, 125 
Magnet cores, 561 
Magnet, electro, 403 
Magnetic attraction, 112 

explained, 120 

mutual, 114 

takes place through intervening 
bodies, 113 
Magnetic blowout, 485 
Magnetic circuit, law of, 400 
Magnetic declination, 169 
Magnetic dip, 171 
Magnetic elements, 175 

variation of, 176 
Magnetic field about wire carrying a 
current, 346, 347, 348 

coil rotating in, 551 



Magnetic field, defined, 134 

determination of strength of, 148, 
149, 150 

direction of, 135 

effect on cathode rays, 673 

effect on positive column, 669 

force exerted upon conductor car- 
rying a current, 356 

graphic representation of intensity 
of, 145 

intensity of, 136 
Magnetic fields, comparison of, 146, 
147 

compounding, 141 
Magnetic figures, 138, 139, 140, 141 

use of, 140 
Magnetic flux, 142 
Magnetic force, 115, 123 
Magnetic forces, measurement of, 127 
Magnetic inclination, 171 
Magnetic intensity, 174 
Magnetic lines of force, 137, 143 

methods of mapping, 138, 139, 141 

pass preferably through magnetic 
substances, 143 

properties of, 142, 143 
Magnetic maps, 170 
Magnetic meridian, 168 
Magnetic moment, 130 
Magnetic needle, polarity of, 116 
Magnetic pole defined, 126 

unit, 133 
Magnetic poles, 110 

inseparable, 111 
Magnetic saturation, 393 
Magnetic screen, 113, 143 
Magnetic shell, 369 
Magnetic storms, 180 
Magnetic substances, 121 
Magnetic variation, 169 
Magnetism, 151 

earth's, theories of, 181 

Ewing's theory of, 153, 395 

free, 142 

intrinsic, 142 

molecular, 152, 395 

residual, 155, 398, 562 
Magnetite arc lamp, 523 



INDEX, 



589 



Magnetization accompanied by molec- 
ular movement, 154 
by divided touch, 163 
by double touch, 163 
by electric current, 164 
by induction, 118, 570 
by single touch, 162 
characteristic, 584 
confined to outer layers of magnet, 

166 
curves of, 394 
cycle of, 398 
effect of heat on, 158 
facilitated by molecular movement, 

155 
facilitated by solution, 159 
facilitated by vibration, 156 
loss facilitated by vibration, 157 
Magneto-motive force, 400 
Make and break, induced E. M. F. 

at, 437 
Manganin, 289 

Manufacture of aluminum, 489 
of calcium carbide, 488 
of carborundum, 488 
of electric lamps, 506 
of magnets, 162, 163, 164 
principle of, 161 
Mapping magnetic lines of force, 138, 

139, 141 
Maps, magnetic, 170 
Marconi, 698, 699, 703 
Mariner's compass, 182 

adjustment of, 183 
Mariotte's law, 256 

osmotic pressure follows, 264 
Mass, unit of, 8 

of corpuscles, 684 
Maximum current from multiple 

grouping, 340 
Maximum flux, law of, 144 
Maximum output of power by motor, 

597 
Maxwell's displacement assumption, 
690 
electro-magnetic theory of light, 548, 

690, 694 
law, 144, 371, 377, 467, 470, 471, 591 



Maxwell's theory, confirmation by 

Hertz, 694, 695 
Mean spherical candle power, 509 
Measure of self induction, 433 
Measurement, absolute, of current, 
374 
of resistance, 542, 546 
Measurement of current by tangent 
galvanometer, 374, 546 
of E. M. F. by voltmeter, 461 
of E. M. F. of cells, 329, 461 
of electric power, 497, 498, 635 
of high resistance, 326 
of internal resistance of cells, 328 
of magnetic forces, 127 
of osmotic pressure, 261 
of power by electro-dynamometer, 

498 
of resistance, 308 

by drop of potential, 309, 310 
by Wheatstone bridge, 317, 318, 
319, 320, 321 
of resistance of electrolytes, 327 
with potentiometer, 332 
Measurements, electrical effects used 
in, 444, 445, 446, 
electro-chemical effect standard for, 

448 
electro-chemical effect unsuited for 

commercial needs, 451 
electro-magnetic effect used in, 452, 

453 
electro-static, 98 
Mechanical potential, 71 
Mechanical production of electrical 

current, 423 
Medium, variation of electric force 

with intervening, 55, 58 
Mercury arc rectifier, 654, 655 
Mercury vapor lamp, 527 
Meridian, magnetic, 168 
Mesh grouping, 646 
Metal, most suitable for making 

magnets, 160 
Meter bridge, 325 
Method by oscillations, 129, 131 
of weakening controlling force of 
galvanometers, 366 



590 



INDEX. 



Methods of self-excitation, 563, 638 
Metric system, 6 
Microhm, 288 
Mil foot, 296 
Millivoltmeter, 473 

as ammeter, 474 
Millivoltmeter shunt, 475 
Mirror galvanometer, 377 
Moissan's furnace, 487 
Molecular magnetism, 152, 395 
Molecular movement facilitates mag- i 
netization, 155 

magnetization accompanied by, 154 
Molybdenite as detector for wireless, 

706 
Moment, magnetic, 130 
Moore light, 526 
Morse, 411 
Morse alphabet, 412 

telegraph, 412 
Motor, 550 

direction of rotation of, 604 

efficiency of, 596 

explanation of motion, 591 

identical with generator, 590 

induction, 428, 662, 663, 664, 665 

maximum output of power by, 597 

power developed by, 592 

power proportional to counter E. 
M. F., 594 

repulsion, 662 

series, 602 
for A. C, 659 
speed of, 603 

shunt, 599 

control of speed of, 600 

synchronous, 660 
operation of, 661 
Motors, alternating current, 657 

classes of, 658 

classes of D. C., 598 
Motor generator, 605, 648, 653 
Moving iron instruments, 464 
Multiple grouping of cells, 339 
Multiplier, 469 

Schweigger's, 365 
Multipolar alternator, 639 
Multipolar generator, 561, 573 



Multipolar generators, advantages of, 

574, 639 
Natural magnets, 105 
Nature of corpuscles, 685 
Needle, dipping, 172 

magnetic polarity of, 116 
Negative electricity, 674 
Negative glow, 670 
Negative ions, 672 
Nernst, 278 
Nernst lamp, 508, 512 
Neutral plane, 551, 570 
Neutral temperature, 529 
No field release, 601 
No voltage release, 601 
Norman, Robert, 171 
Objections to lead batteries, 249 
Observations of Pfeffer, 262, 263 
Oerstedt's discovery, 344, 363 
Ohm, the, 284, 543, 543 

denned in terms of column of mer- 
cury, 291, 543 

international, 291, 543 
Ohm's law, 297, 299, 307, 538 
Open and closed coils, 559 
Operation of synchronous motors, 661 

of telephone, 442 

of transformer, 650 
Oscillations, method by, 129, 131 
Oscillator, 694 

Oscillatory discharge of Leyden jar, 
686, 689 

Feddersen's proof of, 688 

Thomson's proof of, 687 
Osmosis, 259 
Osmotic pressure, 259 

demonstration of, 260 

follows Mariotte's law, 264 

measurement of, 261 

variation of, 263, 264, 265, 266 
Ostwald, 272 
Overcompounding, 589 
Overload switch, 306, 414 
Parallel grouping of cells, 336, 337 

diagrams, 342 
Parallel-series grouping, 339 

diagrams, 342 
Paramagnetics, 122 



INDEX. 



591 



Peltier effect, 530 
Pendulum, electric, 22 
Period, 608 
Permeability, 391, 397 

expression for, 392 
Pfeffer, observations of, 262, 263 
Phase, 609 
Phase difference, 609 
Photometry, 510 
Pierce, 699, 705 
Pile, voltaic, 190 
Pitch blende, 679 
Plane development of drum winding, 

576 
Plante cell, 240 

Plates, storage battery, dimensions of, 
242 

grouping of, 243 

preparation of, 239 
Platinum thermometer, 290 
Points, effect of, 42, 43 

experiments with, 43, 44 
Polarity of electro-magnet, rule for, 

404 
Polarization, 198 
Pole, magnetic denned, 126 

rotation by current, 350 

unit, 133, 535 
Poles, consequent, 165 

earth's, location of, 168 
misnamed, 117 

magnetic, 110 
inseparable, 111 
Polonium, 679 

Polyphase alternators, 640, 644, 645 
Positive column, 668 

effect of magnetic field upon, 669 
Positive rays, 676 
Potential at point due to a charge, 74 

difference, 73 

drop of, 298, 299 

electric, 70, 72, 73, 74, 75, 83 
analogues of, 70 
how measured, 72 

mechanical, 71 

zero, 73 
Potentiometer, arrangement of, 330 

calibration of, 331 



Potentiometer, forms of, 333 

measurement with, 332 
Power, apparent, 635 
defined, 492 

developed by motor, 592 
development in a battery, 495 
electric, absolute unit of, 496 
commercial unit of, 496 
expression for, 494 
measurement of, 497, 498, 635 
practical unit of, 496 
transmission of, 501, 502, 656 
from primary cells, cost of, 343 
in A. C. circuit, 634 
maximum output by motor, 597 
measurement of, by electro-dyna- 
mometer, 498 
of motor proportional to counter 

E. M. F., 594 
tractive, of magnet, 406 
Power E. M. F., 617 
Power factor, 635 
Practical unit of capacity, 95 
of current, 228, 307, 448, 546 
of E. M. F., 427 
of electric power, 496 
of quantity, 228 
of resistance, 284, 546 
of self induction, 433, 434 
Preparation of plates of storage bat= 

tery, 239 
Pressure, variation of resistance with, 
285 
gaseous, laws of variation, 256 
osmotic, 259 

demonstration of, 260 
follows Mariotte's law, 264 
measurement of, 261 
variation of, 263, 264, 265, 266 
Primary cell, 201, 202 

cost of power from, 343 
Primary electro-magnetic units, 538 
Prime conductor, 47 
Primer, electric, 483 
Principle of electrometers, 100 
of induction motor, 663 
of tangent galvanometer, 375 
of wireless telegraphy, 69 S 



592 



INDEX. 



Production of current by rotating coil, 
553 

of rotating field, 664 
Proof plane, 38 
Quadrant electrometer, 103 

theory of, 104 
Quantity, electro-static unit of, 56, 
535 

units of, 536 
Radio-activity, 679 
Radiometer, 533 
Radio-micrometer, 534 
Radium, 679 
Rays, alpha, 679 

Becquerel, 679, 680 

beta, 679 

canal, 676 

cathode, 671, 672, 680 

effect of electric field on, 674 
effect of magnetic field on, 673 

gamma, 679 

Lenard, 677, 680 

positive, 676 

Rontgen, 678 

X, 678, 679, 680, 684 
Reactance, capacity, 628 

inductive, 619 
Reaction, armature, 570, 587 
Reactions of chloride accumulator, 
244 

of Edison battery, 251 
Reactive E. M. F., 619 
Receiving circuit for wireless, 705 

tuning of, 705 
Recording wattmeter, 499, 500 
Rectification of A. C, 556, 653 

of single phase current, 655 
Rectifier, crystal, 705 

electro-chemical, 653 

mercury arc, 654, 655 
Reflecting galvanometer, 378 
Relay, 412, 703, 704, 705 

sensitiveness of, 705 
Reluctance, 391, 400 

specific, 400 
Reluctivity, 400 
Remedy for local action, 197 
Repulsion, electric, 22, 30 



Repulsion motor, 662 
Requirements of arc lamp mechanism, 
517 
of voltaic cell, 200 
Residual charge, 87 
Residual magnetism, 155, 398, 562 
Resistance, 292 

absolute measurement of, 542 
absolute unit of, 427, 546 
critical, 586, 587 
defined, 282 

dimensional formula of, 540 
example of effect of, 283 
expressed as a velocity, 541 
internal, of cells, 294 

measurement of, 328 
joint, 293 

laws of, 285, 286, 287, 288, 289 
measurement of, 308 

by drop of potential, 309, 310 
by Wheatstone bridge, 317, 318, 
319, 320, 321 
of conductors in parallel, 293 
of conductors in series, 286 
of electrolytes, measurement of, 327 
of voltmeter, 458, 459, 460, 461, 

468 
practical unit of, 284, 546 
Siemen's unit of, 543 
specific, 285, 288 
temperature coefficient of, 289 
variation with temperature, 285, 
289 
Resistance and capacity, 629 
Resistance and inductance contrasted, 
616 
effect on alternating E. M. F., 
617 
Resistance and inductance in parallel, 
624 
in series, 623 
Resistance, inductance and capacity, 

630 
Resistances, arrangement of, in bridge, 
315 
measurable by bridge, 324 
Resistance coils, 311 
Resistivity, 292 



INDEX 



593 



Resonance, 631, 632, 633, 697, 701, 
706 
with inductance and capacity in 

parallel, 633 
with inductance and capacity in 
series, 632 
Resonator, 694 

tuning of, 697 
Retentivity, 155 

Reversible ratios, bridge with, 322 
Reversibility of cells, 236 
Revolving armature, alternators with, 

641 
Revolving field, alternators with, 642 
Rheostat, 302, 513, 600 
Right hand rule for deflection of 
needle, 345 
for direction of induced E. M. F., 
422 
Ring transformer, 649 
Ring wound armature, 566 
Ring wound generator, 569 
Rocker frame, 568 
Rontgen rays, 678 
Rotary converter, 653 
Rotating coil, E. M. F. of, 552 
in magnetic field, 551 
production of current by, 553 
Rotating field, production of, 664 
Rotation of current by magnetic pole, 

351 
Rotation of motor, direction of, 604 
Rotation of pole by current, 350 
Rotor, 665 

Rule for direction of field about wire 
carrying current, 348 
for direction of induced E. M. F., 

421, 422 
for direction of motion of wire 

carrying a current, 352 
for deflection of needle by current, 

345 
for polarity of electro-magnet, 404 
Salt, electrolysis of a, 224 
Saturation, magnetic, 393 
Schweigger's multiplier, 365 

graphs, 678 
Screen, magnetic, 113, 143 



Second, mean solar, 9 
Secondary cell, 237 

elements of, 238 
Seebeck's discoveries, 528 
Selenium, 285 

Self-excitation, methods of, 563 
Self-induction, 432, 614 

absolute unit of, 433 

measure of, 433 

practical unit of, 433, 434 
Semicircular variation, 183 
Sensitiveness of relay, 705 

of telephone, 705 
Separation of induced charges, 32 
Series, thermo-electric, 528 
Series generator, 563, 582 

characteristic of, 585 
Series grouping of cells, 335, 337 
Series motor, 602 

speed of, 603 
Series motor for A. C, 659 
Shape of electro-magnets, 407 
Shell transformer, 649 
Shells, magnetic, 369 
Shifting of brushes, 570, 571, 598 
Short circuit, 306 
Shunt, ammeter, 465, 466 

defined, 293 

division of current by, 301 

galvanometer, need of, 380 

milli voltmeter, 475 

switchboard, 466 

universal, 381 
Shunt generator, 563, 582, 587 

characteristic, 587 
Shunt motor, 599 

control of speed, 600 
Siberian oval, 170 
Siemens, 543 
Siemens' electro-dynamometer, 383 

unit of resistance, 543 
Silicon as detector, 706 
Simple cell, 193 

chemical action in, 195 

dissociation theory applied to, 279 
Sine galvanometer, 376 
Sine law, 147 
Single phase alternators, 640, 644 



594 



INDEX. 



Single phase current, rectification of, 

655 
Slide wire bridge, 325 
Slip rings, 642 
Smashing point of incandescent lamp, 

511 
Solenoid, 385 

effect of core on field, 390 

equivalent to bar magnet, 386 

intensity of field on axis, 387 

variation of field with current, 389 
Solution, magnetization favored by, 

159 
Solution tension, 278 
Sounder, 412, 704 
Spark plug, 438 
Sparking, 572 
Specific reluctance, 400 
Specific resistance, 285, 288 
Speed of series motor, 603 

of shunt motor, 600 
Spheres, two coalescing, 82 

two united, 81 
Spider, 565 
Split ring, 556, 567 
Standard cell, Clark's, 212 

need of, 211 

Weston's, 213 
Standard wave length, 706 
Star development of drum winding, 

577 
Star grouping, 647 
Starting box, 601 
Static transformer, 649, 656 
Stator, 665 

Storage battery, charging, 245, 246, 
415, 582 

charging from A. C, 655 

defined, 237 

Edison, 250 

advantages, 253 
charging, 252 
reactions of, 251 

uses of, 254 
Storage battery plates, dimensions, 
242 

grouping of, 243 

preparation of, 239 



Storms, magnetic, 180 
Strength of magnets, 125, 406 
Sturgeon, 403 
Substances, magnetic, 121 

subject to electrolysis, 221 
Surface density of charge, 41, 65, 66 
Suspended coil galvanometer, 378 
Switch, overload, 414 

underload, 414, 582 
Switchboards, 579, 580 
Switchboard shunt, 465, 466 
Symmer's theory of electricity, 27 
Synchronous converter, 653 
Synchronous motor, 660 

operation of, 661 
Table of dimensional formulae, 547 

of magnetic elements, 175 

wire, 295 
Tangent galvanometer, 373, 546 

measurement of current by, 374 

principle of, 375 
Tangent law, 146 
Tantalum lamp, 507 
Telegraph, electric, 411 

Morse, 412 
Telegraph system, American, 413 
Telegraphy, wireless, 698 
Telephone, 440 

in wireless telegraphy, 704, 706 

operation of, 442 

sensitiveness of, 704 
Temperature, absolute, 256 
Temperature of arc, 485 

variation of resistance with, 289 
Temperature coefficient of resistance, 

289 
Tension, solution, 278 

vapor, 277 
Terminology of electrolysis, Faraday's. 

220 
Terrella, Gilbert's, 110 
Theory, dissociation, applied to sim- 
ple cell, 279 
Theory, dissociation, of Arrhenius > 
268 

Grotthus', 274 

of attracted disc electrometer, 102 

of earth's magnetism, 181 



INDEX. 



595 



Theory, etc. — Continued. 

of electrolytic dissociation, extreme 
scope of, 281 

of magnetism, Ewing's, 153, 395 

of quadrant electrometer, 104 
Theories of electricity, 27 
Thermometer, platinum, 290 
Thermopile, 532 
Thermo-couple, 528 
Thermo-electric E. M. F., 528 
Thermo-electric inversion, 529 
Thomson, J. J., 681, 682, 683 
Thomson, Sir William, see Kelvin 
Thomson effect, 531 
Thomson inclined coil instruments, 

471 
Thomson's proof of oscillatory dis- 
charge, 687 
Three wire system, 581 
Thunder storm, explanation proposed, 

82 
Time, unit of, 9 
Toepler's influence machine, 49 
Torsion, law of, 52, 127 
Torsion balance, Coulomb's, 52, 100, 

127, 132 
Tractive power of magnet, 406 
Transformation of D. C. and A. C, 

648 
Transformer, 431, 649 

auto, 652 

core, 649 

Faraday's ring, 431 

operation of, 650 

ring, 649 

shell, 649 

static, 649, 656 

step down, 431 

step up, 431 
Transformers, connection of, 651 

use with A. C. instruments, 472 
Transmission of power, electrical, 501, 

502 
Transmitter, Blake, 441 

wireless, 700 
Tri-phase alternator, 645, 646, 647 
Tri-phase delta grouping, 646 

Y connection, 647 



Troubles of lead batteries, 247 
Tube, Crookes', 670, 671, 672, 675, 
676, 677, 678, 682 
focusing, 678 
Geissler, 670 
Tubes of force, 62 
Tungsten lamp, 507, 512 
Tuning of coupled circuits, 702 
of receiving circuits, 706 
of resonator, 697 
Turning moment of magnet, 149 
Ultra-violet light, 680 
Underload switch, 415, 582 
Unit of capacity, practical, 95 
of current, 536 

absolute, 355, 536, 546 
practical, 228, 307, 448, 546 
of E. M. F., 537 

absolute, 426, 537, 546 
practical, 77, 427 
of electric power, absolute, 496 
commercial, 496 
practical, 496 
of electric work, commercial, 496 
of force, 11 
of heat, 11, 478 
of length, 7 
of mass, 8 
of quantity, 536 
practical, 228 
of resistance, absolute, 427, 546 
practical, 284, 546 
Siemens', 543 
of self-induction, absolute, 433 

practical, 433, 434 
of time, 9 
of work, 11 
Units, absolute, 11 
electro-magnetic, 535 

primary, 538 
electro-static, 535 
fundamental, 3 
Unit charge, lines of force from, 63 
Unit electric field, 58, 61 
Unit jars, 99 
Unit magnet pole, 133 
Unit quantity of electricity, 56 
Universal shunt, 381 



596 



IXDEX. 



Use of electro-magnets, 408 

of storage batteries, 254 
Useful volts, 305 

Vacua, discharge through high, 670 
Vacuum tubes, 707, 70S, 709 
Value of alternating current, 612, 613 
Value of electro-magnet, 405 
Van't Hoff's generalization, 266 

exceptions to, 267 
Vapor tension, 277 
Variation, magnetic, 169 
Variation of magnetic elements, 176 

of osmotic pressure, 263, 264, 265, 
266 

semicircular, 183 
Vector diagram, 610 
Velocity, resistance expressed as a, 541 

of corpuscles, 683 

of propagation of electric wave, 693, 
694 
Versorium, 16 

Vibration, loss of magnetization facili- 
tated by, 157 

magnetization facilitated by, 156 
Virtual amperes and volts, 612 
Volt, 77, 78, 427, 537, 545, 546 

denned, 307, 427, 545, 546 

international, 212 
Volts, lost and useful, 305 

virtual, 612 
Volta, 35, 186, 187, 188, 190, 191, 218. 
Volta's circlet of cups, 191 

contact series, 187 

contact theory, 188 

investigations, 186 
Voltaic cell, requirements of, 200 
Voltaic pile, 190 
Voltameter, 227 

Voltmeter, 455, 458, 459, 460, 468, 
470, 471, 472 

connection of, 458, 459 

measurement of E. M. F. by, 460, 
461 

reading across counter E. M. F., 595 

resistance of, 458, 459, 460, 461, 468 

Weston D. C, 468 

Weston D. C. A. C, 470 
Voltmeters classified, 462 



Water, decomposition of, 218 

electrolysis of, 219 
Watt, 493 
Watt, the, 496 
Wattmeter, indicating, 499 

integrating, 500 

recording, 499, 500 
Waves, electric, 690, 694, 703 

length of, 696, 702 

velocity of propagation, 693 
Wave length, standard, 706 
Wave meter, 702 
Wave winding, 575 
Weber, 153 

Weber's electro-dynamometer, 382 
Weights, lifting by electro-magnets, 

409 
Welding, electric, 484 
Weston A. C. ammeter, 467 

D. C. voltmeter, 468 

D. C. A. C. voltmeter, 470 

standard cell, 213 
Wheatstone bridge, arrangement of 
resistances, 315 

evolution in form, 316 

measurement of resistances by, 317, 
318, 319, 320, 321 

principle of, 313, 314 
Whirl, electric, 44 
Wind, electric, 42, 44, 48, 49, 50 
Wire carrying a current not a magnet, 

349 
Wire, circular measure of, 296 
Wires, electric heating of, 480, 481 
Wire gauges, 295 
Wire tables, 295 
Wireless telegraphy, 698 

condition affecting, 707 

distance attained by, 707 
Work done by electric current, 476 
Work in moving coil across field, 358 

in moving conductor across field, 357 
Work, unit of, 11 

electric, commercial unit of, 496 
X rays, 678, 679, 680, 684 
Y connection, 647 
Yoke, 561 
Zincite as detector, 706 



PROBLEMS 



CHAPTER 1. 

1. a. A gallon is 277.28 cubic inches: a cubic foot of water weighs 

62.34 pounds. How many gallons and what is the weight 
of the water contained in a tank which measures 2 ft. 7 in. by 
3 ft. 4 in. by 1 ft. 5 in.? 
b. A second tank is 87 centimeters by 1 meter and 2 cms. by 43 
cms. What is its capacity in cubic centimeters; how many 
litres of water will it contain and what is the weight of this 
water in kilograms? 

2. The specific gravity of sulphuric acid is 1.834; what is the weight 

in grams of a litre of the acid? 

3. A bar of \ copper 2x3x1/2 centimeters weighs 26.79 grams. 

What is its specific gravity? 

4. a. The average barometric pressure is 1035.69 grams per square 

centimeter. What is the height of the column of water that 
this pressure will sustain? 

b. Had this pressure been given in pounds per square inch, 

what additional data would the solution of the problem 
have required? 

c. The specific gravity of mercury is 13.59; what is the height 

in millimeters of the average barometric column? 

5. The specific gravity of mercury is 13.59; what volume in absolute 

units is occupied by 122.31 grams? 

6. The weight of one gram corresponds to 981 dynes; one kilogram 

weighs 2.2046 pounds; one meter equals 39.37 inches; the 
mechanical equivalent of the British thermal unit is 1402 
foot pounds. 

a. What is the equivalent in dynes of the practical unit of force 

in the English system? 

b. What is the equivalent in absolute units of the English prac- 

tical unit of work? 

c. What is the equivalent in terms of the absolute unit of work 

of the small calorie? 



CHAPTER 3. 

7. a. How can a charged conductor be discharged? 

b. How can a charged non-conductor be discharged? 

8. Explain how by means of an electric pendulum we may determine: 

a. Whether a body is charged or not. 

b. Whether it is charged positively or negatively. 

9. a. Define conductors and non-conductors. 

b. Name some good conductors. 

c. Name some insulators. 

d. If a positive charge be produced upon a body by rubbing, how 

large a negative charge will be produced upon the rubber? 

e. How may this be shown? 

10. a. What effect have like charges of electricity upon each other? 

b. What effect have unlike charges upon each other? 

c. What is an electroscope? 

d. If two bodies rubbed together acquire opposite charges, how 

may the equality of these charges be shown? 



CHAPTER 4. 

11. a. A positively charged body is held near one end of an elongated 

conductor. The conductor is then parted at the center by 
means of insulated supports. Are the separate parts charged 
and if so, how? 

b. The charged body is withdrawn and the two parts of the 

elongated conductor are brought into contact. What is now 
the condition of the parts? 

c. What determines the amount of charge that may be produced 

by influence? 

12. a. Make a diagram showing conditions of electrification when a 

charged body is brought near an insulated conductor. 

b. Mark the free and the bound charges. 

c. Touch the insulated conductor with a piece of iron. What 

happens? 

d. Is the conductor now charged; if so, how? 

e. What happens if the conductor be touched with a glass rod? 
/. Is the conductor now charged; if so, how? 



13. a. a and b represent two conductors separated by a glass plate. 
a has a positive charge, b has a negative charge, 
and the charges are bound. What happens if a 
is touched? 
" b. What happens if 6 is touched? 

c. What happens if a and 6 are touched simultane- 
ously? 

14. a. In the figure above, a and b are two glass plates separated by a 
plate of ebonite, a is charged positively, b is charged nega- 
tively, and the charges are bound. What happens if a is 
touched? 

b. What happens if b is touched? 

c. What happens if a and b are touched simultaneously? 

15. a. Make a diagram of a gold leaf electroscope, r naming parts. 

b. Explain how by means of this instrument we can determine 

whether a body is charged or not. 

c. Explain how we may determine the nature of the charge. 

16. a. Make a diagram indicating the method of charging a gold leaf 

electroscope positively by means of a positively electrified rod. 
b. Make a diagram indicating the method of charging it nega- 
tively by means of a positively electrified rod. 

17. a. Make a diagram indicating the method of charging a gold leaf 

electroscope negatively by means of a negatively electrified rod. 
b. Make a diagram indicating the method of charging it positively 
by means of a negatively electrified rod. 

18. a. Make a diagram of an electrophorus, naming parts and giving 

material of which they are made. 

b. Explain its operation. 

c. After giving the instrument the initial charge, how many dis- 

charges may be obtained? 

d. What is the source of the energy which produces these dis- 

charges? 

19. a. Assume the upper surface of the electrophorus to be charged 

positively . Put on the cover. What happens? Indicate by 
a diagram. 

b. What happens if the cover be touched? 

c. If the cover be raised, is it acted upon by any force? If so, 

in what direction would the force tend to move it? 

d. Is the cover charged; if so, how? 

e. State the general principle involved when a conductor is touched 

while under the influence of a charged body. 



CHAPTER 5. 

20. a. An insulated hollow sphere is touched by a negatively charged 

conductor. Is the sphere now charged; if so, how? 

b. An insulated metal disc is now touched to the inside of the 

sphere. Is the disc charged; if so, how? 

c. Give reasons for answers. 

CHAPTER 6. 

21. a. By what means is the charge of electricity generated in the 

friction machines? 

b. Make a diagram of the cylinder machine with prime conductor. 

Mark the charges on both. 

c. Explain the principle by which the prime conductor is charged. 

CHAPTER 7. 

22. a. Equal and similar charges imparted to the balls of the torsion 

balance cause the needle to move through an angle of 10°. 
When the torsion head is turned in contrary direction through 
an angle of 35°, the needle is brought back to an angle of 5°. 
What is now the angle of torsion? 
b. Deduce from this observation the law of variation of electric 
repulsion with distance. 

23. A charge imparted to the balls of the torsion balance causes the 

needle to move through an angle of 16°. Through what angle 
must the torsion head be twisted in order to bring the needle 
back to an angle of 4°? 

24. a. Give the general expression for the force between two charged 

bodies, explaining the meaning of each term. 

b. Define the electrostatic unit quantity of electricity. 

c. How does this quantity compare with a coulomb? 

25. Two small charged insulated spheres repel each other with a force 

of three dynes. The charge on one is doubled and the dis- 
tance between the spheres is doubled; with what force do 
they now repel each other? 

26. Two small insulated spheres are charged and placed 5 cms. apart 

in air. They repel each other with a force of 8 dynes. The 
charge on one sphere is twice that on the other. Find the 
charges. 



27. Find the distance apart in air that two spheres charged with +2 

and +32 units of electricity must be placed so that they will 
repel each other with a force of 4 dynes. 

28. a. A small insulated sphere is charged with +18 units of electricity. 

With what force will it act upon a charge of +2 units placed 
at a distance of 3 cms. in air? 
b. At what distance must the +2 units be placed so that the force 
is one dyne? 

29. a. Two small insulated spheres of the same size are charged with 

+6 and +4 units of electricity respectively. With what 
force will they act upon each other if placed 3 cms. apart 
in air? 

b. Is this a force of attraction or of repulsion? 

c. The spheres are brought into contact and then restored to their 

original positions. With what force do they now act upon 
each other? 

d. Is this a force of attraction or of repulsion? 

30. a. Two small insulated spheres of the same size are charged with +15 

and — 5 units of electricity respectively. With what force will 
they act upon each other if placed 5 cms. apart in air? 

b. Is this a force of attraction or of repulsion? 

c. The spheres are brought into contact and then restored to their 

original positions. With what force do they now act upon 
each other? 

d. Is this a force of attraction or of repulsion? 

31. a. Two small insulated spheres of the same size are charged with 

— 15 and +5 units of electricity respectively. With what force 
will they act upon each other if placed 5 cms. apart in air? 

b. Is this a force of attraction or of repulsion? 

c. The spheres are brought into contact and then restored to their 

original positions. With what force do they now act upon 
each other? 

d. Is this a force of attraction or of repulsion? 

32. a. A small insulated sphere charged with 4-8 units of electricity 

and placed at a distance of 5 cms. from a similar sphere is 
attracted with a force of 1.5 dynes. What is the charge on 
the second sphere? 
6. What would be the force between the spheres had they been 
immersed in oil, the charges and the distance apart remain- 
ing unchanged? 



CHAPTER 8. 

33. a. Define a unit electrical field. 

b. What is meant by a field of strength H ? 

c. With what force will a field H act upon a charge q placed in it? 

34. a. A small sphere is charged with +15 units of electricity. With 

what force will it act upon a charge of +2 units at a distance 
of 3 cms.? 
b. What is the intensity of the field at the position of the 2 units? 

35. Draw a diagram of the lines of force emanating from three posi- 

tively charged spheres placed at the vertices of an equilateral 
triangle. 

36. Draw a diagram of the lines of force emanating from three spheres 

placed at the vertices of an equilateral triangle, two being 
charged positively and one negatively. 

37. a. A positively charged sphere suspended by a silk thread hangs 

within a metal pail. Make a diagram of the field, supposing 
the pail to rest on an insulated stand. 
b. Make a diagram of the field, supposing the pail to be connected 
with the ground. 

38. a. A positively charged sphere suspended by a silk thread hangs 

within a metal pail and near the bottom. The pail is on an 
insulated stand but is connected to the knob of a gold leaf 
electroscope. Make a diagram of the field. 

b. The ball is lowered until it touches the pail. What happens? 

c. How is the electroscope affected? Give reasons for answer. 

39. Equal and opposite charges are placed at the extremities of the 

horizontal base of an equilateral triangle. Find the direction 
of the line of force through the vertex of the triangle. 

40. a. Define a unit electrical field. 

b. What is the space around a charged body called? 

c. What is a line of force? 

d. What is the positive direction of a line of force? 

41. a. Define a unit electrical field in terms of the force exerted upon 

a charge. 

b. With what force will a charge of 8 units be acted upon if placed 

in a field whose strength is 0.3? 

c. Define a unit field in terms of the number of lines of force em- 

braced. 

d. What is the positive direction of a line of force? 



42. a. Give the general expression for the force exerted between two 

charged bodies. 

b. Deduce from this the definition of the electrostatic unit quan- 

tity of electricity. 

c. At what distance from a charge of 10 units is there a unit 

field? 

d. Define a line of force. 

43. a. Two small spheres of equal size are charged with +15 and —5 

units of electricity respectively. With what force will they 
act upon each other if placed 5 cms. apart in air? 

b. Make a diagram of the field. 

c. Make a diagram showing the field had the charges been 

similar. 

44. a. Define an electrostatic unit quantity of electricity. 

b. Define in terms of lines of force a unit field. 

c. At what distance from a unit quantity of electricity is there a 

unit field? 

d. How many lines of force emanate from a unit quantity of 

electricity? 

e. At what distance from a charge of 4 units of electricity is there 

a unit field? 

45. a. A plane of indefinite extent is charged to a surface density of 5 

units of electricity per square centimeter. With what force 
will it act upon a charge of 4 units placed at a distance of 3 
centimeters? 
b. What is the effect upon the force if the distance be decreased 
to 2 centimeters? 

46. As a thunder storm passes over a pond, the surface of the water 

rises one-tenth of a centimeter. Find the surface density of 
the charge induced upon the water. 

CHAPTER 9. 

47. a. A charge of 30 electrostatic units is moved from a point whose 

potential is 10 to a point whose potential is 25. Find the 
work done. 
6. 75 ergs are expended in moving 3 units of electricity from a 
point whose potential is —5 to a point whose potential is 
positive. Find the potential of the second point. 



8 

48. a. Make a diagram of the equipotential surfaces surrounding a 

small positively charged sphere. 

b. The potential at one of the surfaces is 3; what does this mean? 

c. The sphere is charged with 6 units of electricity. At what dis- 

tance is the above equipotential surface from the center of 
the sphere? 

d. If a body charged with 3 units of electricity be moved about on 

this equipotential surface, how much work will be done? 

49. a. What is the potential at a point 20 cms. distant from a sphere 

charged with 15 units of electricity? 

b. What does this mean? 

c. What is the potential at a point 30 cms. distant? 

d. What is the difference of potential between the two points? 

e. How much work would be done in moving 5 units of positive 

electricity from one point to the other? 

50. a. Three charges of electricity of +10, +12 and —8 units are 

placed at distances of 5, 7 and 11 cms. respectively from a 
point A . What is the potential at this point? 
6. Bring all three charges together at a distance of 10 cms. from 
the point. What is now the potential at A? 

51. a. Upon three corners of a square whose sides are 10 centimeters 

are placed charges of 20, 30 and 40 units respectively. Find 
the potential at the fourth corner. 

b. Find the potential at the intersection of the diagonals of the 

square. 

c. What is taken as the measure of the difference of the potential 

between two points? 

52. a. A sphere of radius R is given a charge of Q units. What is the 

potential of a point on the surface of the sphere? 

b. What force is exerted by this charge at a point on the interior 

of the sphere? 

c. What work is done in moving a unit charge between two points 

on the interior of the sphere? 

d. What is the difference of potential between these points? 

e. What is the potential at any point on the interior of the sphere? 

53. a. The difference of potential between two points is 20. In what 

unit is this expressed? 

b. What does it mean? 

c. The distance between the two points is 5 cms. What is the 

average electric force between the points? 



54. a. A small sphere has a charge of 6 units of positive electricity. 

What is the potential at a point P, 3 cms. distant from the 
center of this sphere? 

b. What work is required to bring a charge of 5 units of positive 

electricity from the point P to a point P', 2 cms. distant 
from the center of the sphere? 

c. What is the potential difference in volts between P and P'l 

55. a. Two parallel planes of indefinite extent and 2 centimeters apart 

are charged, one to a surface density of +6, and the other of 
+3. In what direction and with what force will a unit posi- 
tive charge placed between the planes be acted upon? 

b. What work will be done in moving a unit positive charge from 

one plane to the other? 

c. What is the difference in potential in volts between these planes? 

CHAPTER 10. 

56. a. A spherical conductor of 5 cms. radius is charged with 15 units 

of positive electricity. What is the potential at its surface? 

b. What does this mean? 

c. How much work will be done in moving a unit of positive elec- 

tricity across the diameter of the sphere? Give reason for 
answer. 

57. a. Find the quantity of electricity required to charge a sphere of 

10 cms. radius until its surface density is 5. 
b. Find the potential of the surface of the sphere. 

58. a. Find the potential to which an insulated metal sphere of 3 cms. 

radius is raised by a charge of 24 units. 
b. Find the charge that must be imparted to a similar sphere of 
2 cms. radius so that when the two spheres are connected by 
a wire there will be no flow of electricity between them. 

59. a. A sphere whose radius is 8 centimeters is charged to a surface 

density of 10. What quantity of electricity does it carry? 

b. Find the force that this charge will exert upon a unit charge 

very near the surface of the sphere. 

c. Find the potential of the sphere. 

60. a. An insulated sphere A whose radius is R is given a charge Q. It- 

is then touched to a second insulated sphere B whose radius 
is r. Find the charges on the two spheres. 

b. Find the surface density of the charges on the spheres. 

c. Find the potentials of the two spheres. 



10 

61. a. A sphere of 2 cms. radius is given a charge of 6 units of positive 

electricity. To what potential is the sphere raised? 
b. It is touched against an insulated sphere whose radius is 0.2 cm. 
What is the surface density of the charge upon the smaller 
sphere? 

62. a. A sphere whose radius is 8 cms. is given a charge of 12,566 units 

of electricity. Find its surface density and its potential. 
b. It is touched to an uncharged insulated sphere whose radius is 
12 cms. and the two spheres are then separated. Find the 
charges, surface densities and potentials of the two spheres. 

63. To spheres of 3 and 5 cms. radius are given charges of 8 and 12 

units respectively. Suppose the spheres to be then touched 
together and separated. Find the charge on each and the 
potential of each. 

64. a. What is the capacity of a sphere? 

b. How does it vary? 

c. Make a diagram of 2 spheres of 10 and 2 cms. radius respec- 

tively. Suppose these to be connected by a wire. If a charge 
of 50 units of electricity be imparted to the smaller, how will 
it be distributed between the two spheres? 

d. Calculate the surface density of the charge on each. 

e. How do these surface densities vary? 

/. If the smaller sphere be reduced to a point, what happens? 

65. a. Make a diagram of a negatively charged Ley den jar on an in- 

sulated stand. Name the materials used and indicate the 
distribution of the electricity. 

b. What happens if the knob of the jar be touched? Why? 

c. What happens if the outside coating of the jar be touched and 

why? 

d. What happens if the knob and the outside coating be touched 

simultaneously? Why? 

66. a. Make a diagram showing a plate of ebonite separating an insu- 

lated conductor A from a positively charged body B, this 
latter being connected to a source of electricity. 

b. Let B approach A. What is the effect on A? 

c. What is now the effect of connecting A to earth? 

d. What is this arrangement called? 

e. What is its object? 



11 

67. The outer coating of a Leyden jar is grounded and a charge of 

3600 units is given to the inner coating. The potential of the 
inner coating is thereby raised to 12. Find the capacity .of 
the jar. 

68. A spherical condenser consists of two concentric spheres of 10 

and 11 cms. radius respectively, the dielectric being air. To 
what potential is it raised by a charge of 275 electrostatic 
units? 

69. An insulated conducting sphere of 3 cms. radius is connected by a 

wire to a second similar sphere of 5 cms. radius. The second 
sphere is surrounded but not touched by a third whose radius 
is 6 cms. Find the capacity of the combination. 

70. a. What is a condenser? 

b. What is meant by the capacity of a condenser? 

c. What determines the capacity of a condenser? 

d. What determines the amount of charge that can be imparted 

to a condenser? 

71. a. Make a diagram of a positively charged Leyden jar on an insu- 

lated stand. Name the materials used and indicate the dis- 
tribution of the electricity. 
6. What happens if the outside of the jar is connected to 
earth? 

c. Is the jar now capable of holding a greater or less charge than 

before? 

d. What determines the amount of charge that can be imparted to 

a Leyden jar? 

72. a. What is the capacity of a conducting sphere whose diameter 

is 30 centimeters (about one foot)? 
6. This is surrounded by a concentric conducting sphere which is 
connected to earth and separated from the interior sphere by 
a distance of 2 millimeters, the intervening space being filled 
with oil whose dielectric capacity is 3. What is the capacity 
of the arrangement? 

73. A sphere whose capacity is 5 is surrounded by a concentric sphere 

which is earth connected. The space between the two spheres 
is one centimeter in thickness. This is filled with melted shellac 
and by measurement the capacity is now found to be 90. 
What is the dielectric capacity of shellac? 



12 

74. Find the distance by which two circular metallic discs of 3 cms. 

radius must be separated in air so that their capacity is the 
same as that of a sphere of 36 cms. radius. 

75. A condenser consists of a sheet of mica 0.1 millimeter in thickness, 

upon whose face are pasted circular sheets of tin-foil whose 
radius is 5 centimeters. The dielectric capacity of the mica 
is 7. Find the capacity of the condenser. 

76. a. Calculate the capacity of a plate condenser made of two sheets 

of tin-foil, each of 100 square centimeters area, pasted on 
the opposite sides of a pane of glass 1 millimeter in thickness 
and of a dielectric capacity of 3. 
b. If a sheet of ebonite 5 millimeters thick and of a dielectric 
capacity 2 be used instead of the glass, find the area of the 
tin-foil sheets in order that the capacity may be the same. 

77. A glass globe whose inner diameter is 10 cms. and whose thickness 

is 2 millimeters is silvered inside and out. The outer coat- 
ing is connected to the earth ; the inner to a source of electric- 
ity. The dielectric capacity of the glass is 5. Find the 
capacity of the globe. 

78. The dielectric capacity of mica is 8. The thickness of a given 

sheet is one-hundredth of a centimeter. Find the diameter 
of the circular discs of tin-foil which when pasted on opposite 
sides of this sheet form a condenser of the same capacity as 
that of a sphere whose diameter is 1 meter. 

79. A spherical condenser with shellac as a dielectric is charged to a 

potential of 15. Its knob is then touched to the knob of a 
second condenser exactly similar to the first except that the 
dielectric is paraffine. Both condensers now have a potential 
of 9. If the dielectric capacity of paraffine is 2, find what it 
is for shellac. 

80. a. A spherical condenser consists of two concentric spheres of 2.5 

and 3 cms. radius respectively, the dielectric being air. Find 
the work done in transferring 20 electrostatic units to the 
condenser. 
b. Find the potential to which the condenser is raised. 

81. A spherical condenser consists of two concentric spheres of 7.5 and 

8 cms. radius respectively, the dielectric being air. It is 
given a charge of 700 electrostatic units. Find the work done 
when the condenser is discharged. 



13 

CHAPTER 12. 

82. a. Make a diagram of a bar magnet and letter its poles. 

b. Approach the north end of the magnet with the north end of a 

magnetic needle. What happens? 

c. Approach the south end of the magnet with the north end of 

the needle. What happens? 

d. Repeat these experiments, using the south end of the needle. 

e. State the law of magnetism founded on these observa- 

tions. 

83. a. Make a diagram of a magnetic needle freely suspended at its 

center. Mark its poles. 

b. Indicate the position of the north pole of the earth. 

c. What is meant by the north -seeking pole of the needle? 

d. If free to move, where would it go? 

84. a. Make a diagram of a bar magnet and letter its poles. 

b. If a piece of soft iron be brought near the north pole, what action 

takes place? 

c. Reverse the magnet end for end and explain what takes 

place. 

85. a. The north end of a magnet is touched to a piece of soft iron. 

Explain what happens and why. 
b. Represent a column of soft iron standing vertically in the 
northern hemisphere. Explain what happens magnetically to 
the column and why? 



CHAPTER 13. 

86. Two magnetic needles of the same size and weight and freely sus- 

pended under the earth's action at the same locality make 45 
and 47 oscillations respectively in the same time. Compare 
their magnetic strength. 

87. A magnetic needle at a certain locality made 11 oscillations per 

minute under the influence of the earth's magnetism. It was 
accidentally dropped and when the above experiment was re- 
peated it made only 9 oscillations per minute. How much of 
its original pole strength had been lost? 



14 

88. A magnetic needle at a certain locality made 7 oscillations per 

minute under the influence of the earth's magnetism. It was 
remagnetized until its pole strength was twice as great as 
before. How many oscillations per minute will it now make? 

89. A magnetic needle makes 13 vibrations per minute when exposed 

to the earth's field a one. When the north pole of a certain 
magnet is held in the meridian north of the needle, the num- 
ber of vibrations is reduced to 7. Find the number when the 
north pole of this magnet is held at an equal distance to the 
south of the needle. 

90. A magnetic needle which at Washington made 10 oscillations per 

minute under the influence of the earth's magnetism was 
taken to Galveston, where it made 12 in the same time. The 
intensity of the horizontal component of the earth's magnet- 
ism at Washington is 0.2; what is it at Galveston? 

91. A magnetic needle is suspended from the vertical wire of a torsion 

balance. When the torsion head is turned through an angle 
of 75°, the needle is deflected 15° from the meridian. The 
needle having lost its magnetism is remagnetized. The tor- 
sion head must now be turned through 105° to produce a de- 
flection of 15°. Find the pole strength of the remagnetized 
needle as compared to the original pole strength. 

92. a. Represent a magnetic needle inclined at an angle x° to the mag- 

netic meridian through its pivot. Indicate the action lines 

upon the poles of the needle of the horizontal component of 

the earth's magnetism. 
6. The strength of the poles of the needle is 6; the horizontal 

component of the earth's magnetism is 0.23. Find the force 

exerted upon each pole, 
c. Construct the components which tend to restore the needle to 

the meridian and find their value. 

93. a. Make a diagram of a magnetic needle deflected 15° from the 

meridian by a string, one end of which is attached to the N 
end of the needle and the other end pulled to the southeast 
at an angle of 45° with the meridian. Represent the action 
lines of the forces acting upon the needle and construct their 
active components. 
6. The strength of the pole of the needle is 2 and the horizontal 
component of the earth's magnetism is 0.18. Find the pull on 
the string. 



15 

94. A magnetic needle makes 10 oscillations per minute under the 

influence of the earth's field. A bar magnet is placed in the 
magnetic meridian through the needle with its poles in the 
same direction as those of the needle. The needle now makes 
12 oscillations per minute. How many will it make if the bar 
magnet be turned end for end? 

95. a. Two equal magnetic poles placed 6 cms. apart exert on each 

other an attraction of 4 dynes. Find the strength of the 
poles. 
b. Are the poles similar or dissimilar? 

96. Two magnetic poles 20 cms. apart repel each other with a force of 

one dyne. Find the distance at which the repulsion will be 
8 dynes. 

97. Two magnetic poles 6 cms. apart repel each other with a force of 

20 dynes. Find the distance at which they will repel each 
other with a force of one dyne. 

CHAPTER 14. 

98. a. Define a unit magnetic field. 

b. A magnetic pole has a strength of 50. At what distance from 
this pole is there a unit field? 

99. a. Define the positive direction of a magnetic field. 

b. Define the intensity of a magnetic field. 

c. At what distance from a pole of 10 units strength is there a 

unit field? 

d. What is meant by the statement that the intensity of a mag- 

netic field is HI 

100. a. With what force would a field H act upon a pole of strength m 

placed in it? 

b. With what force would a pole of strength q act upon the pole 

m at a distance of r cms. from it? 

c. What is the relation between a magnetic pole and the field pro- 

duced by it at a distance r? 

101. A slender bar magnet is placed both in the magnetic meridian and 

in the horizontal plane through the center of a horizontally 
suspended magnetic needle. The needle is given a slight 
impulse and makes 17 oscillations in one minute. The bar 
magnet is now reversed but otherwise retains the same position 
as before. The needle now makes 7 oscillations per minute. 
Find the number it will make per minute if the bar magnet 
be taken away. 



16 

102. a. Make a diagram of a magnet and mark its poles. 

b. What is the space around the magnet called? 

c. Draw three complete lines of force. 

d. Indicate the positive direction of these lines. 

e. If a free north-seeking pole be placed near the magnet, what 

will it do? 

103. a. Make a diagram of two magnets, the north pole of one near 

the south pole of the other. 

b. Sketch the resulting field, making three complete lines of 

force. 

c. Indicate by arrowheads the positive direction of these lines. 

d. Place a free south-seeking pole on one of them and indicate the 

direction in which it would move. 

104. a. Make a diagram of two magnets with north poles near each 

other. 

b. Sketch the resulting field, making three complete lines of 

force. 

c. Indicate by arrowheads the positive direction of these lines. 

d. What is meant by the positive direction of a line of force? 

105. a. Define a unit magnetic field. 

b. Do magnetic lines of force ever intersect each other? 

c. How do magnetic lines of force terminate? 

d. Draw a magnet with three complete lines of force. 

e. Indicate the positive direction of these lines. 

/. Indicate by a diagram the lines of force in a uniform field. 

106. An iron ball suspended by a wire from a bridge so that the ball 

is immersed in the stream is swept by the current until the 
wire makes an angle of 10° with the vertical. On the occur- 
rence of a freshet, this angle is increased to 15°. Compare 
the force of the current on the two occasions. 

107. a. A magnetic needle is deflected from the magnetic meridian by a 

magnetic force acting constantly at right angles to the merid- 
ian. Make a diagram of the needle in its position of equi- 
librium, indicating deflecting force. 

b. Indicate the controlling force. 

c. Indicate the active component of the controlling and of the 

deflecting forces. 

d. Give the expressions for the values of these active com- 

ponents. 



17 

108. A long bar magnet placed at a distance due east of the pivot of a 

small magnetic needle, its axis perpendicular to the magnetic 
meridian, causes in the needle a deflection of 30°. A similar 
bar magnet placed in the same position as the first causes a 
deflection of 60°. How does the pole strength of the first 
magnet compare with that of the second? 

109. a. Make a diagram of a magnetic needle deflected x° from the 

meridian by a non-magnetic force acting constantly at right 
angles to the meridian. 

b. Find the value of the controlling force and of its active com- 

ponent. 

c. Find the value of the deflecting force. 

d. Does the deflection vary with the strength of the needle? 

110. a. Make a diagram of a magnetic needle deflected by a non- 

magnetic force acting at an angle of x° with the meridian. 

b. Equate the expressions for the active components of the deflect- 

ing and the controlling forces and show whether the deflection 
varies with the length of the needle or not. 

c. Show whether it varies with the strength of the needle or not. 

111. a. Make a diagram of a magnetic needle deflected 15° from the 

meridian by a non-magnetic force acting at an angle of 45° 
with the meridian. 

b. The pole strength of the needle is m. Find the value of the 

controlling force and of its active component. 

c. Find the value of the deflecting force. 

112. a. Make a diagram of a magnetic needle deflected x° from the 

magnetic meridian by a magnetic field acting constantly at 
right angles to the needle. 

b. Give the value for the controlling field and for the controlling 

force. 

c. What is the value of the active component of the controlling 

force? 

d. What is the value of the deflecting field and of the deflecting 

force? 

113. a. Make a diagram of a magnetic needle of pole strength m de- 

flected 15° from the meridian by a magnetic field making a 
constant angle of 60° with the needle. 

b. Find the value of the active component of the controlling force. 

c. Find the value of the deflecting field. 



18 

114. a. Make a diagram of a magnetic needle deflected x° from the 

magnetic meridian by a non-magnetic force acting constantly 
at right angles to the needle. Represent this force by F. 

b. What is the value of the active component of the controlling 

force? 

c. What is the value of F? 

CHAPTER 17. 

115. a. A dipping needle at a certain locality stands at an angle of 60°. 

A small weight is attached to its upper end and reduces the 
angle of dip to 45°. Make a diagram of the needle showing 
the action lines of the forces acting upon it. 
b. Find the expressions for the active components of these forces. 

116. At Albany where the horizontal intensity of the earth's magnetism 

is 0.169, a magnetic needle makes 11 vibrations per minute. 
How many would it make per minute if taken to Silver City, 
New Mexico, where the horizontal intensity is 0.273? 

117. A magnetic needle which made 40 vibrations in a certain period 

at Washington made 48 in the same period at Key West. 
The horizontal component of the earth's magnetism at Wash- 
ington is 0.20 and the dip at Key West is 55°. Find the total 
magnetic intensity at Key West. 

118. a. A vessel built in Scotland has a steel cut- water and a steel 

stern post. Make diagrams of this vessel sailing towards the 
four cardinal points. Place on each of these diagrams a 
compass and show in which of these positions the compass is 
affected. 

b. What effect will these disturbances have upon the course of 

the vessel? 

CHAPTER 19. 

119. a. Make a diagram of a simple voltaic cell. Name and mark the 

materials employed. 
6. Complete the circuit. Mark the positive and negative poles 
and indicate the direction of flow of current in the external 
circuit. 

c. The difference of potential between the liquid and one of the 

poles is 0.5; that between the liquid and the other pole is 
1.50; what is the E. M. F. of the cell? 



19 

120. a. Two copper plates are immersed in a cell containing dilute 

sulphuric acid and the circuit is completed. Will a current 
flow? Give reason for answer. 

b. A copper and a zinc plate are then immersed in the cell and the cir- 

cuit is completed. Will a current flow? Give reason for answer. 

c. Make a diagram of the cell, indicating the positive and negative 

poles and the direction of flow of current in the external circuit. 

d. What is the source of energy of the voltaic current? 

121. a. Make a diagram of a simple voltaic cell, naming and marking 

the materials employed. 

b. Mark the positive and negative poles and indicate the direction 

of the current in the external circuit. 

c. Write the reaction which takes place in the cell and indicate 

what becomes of the products of this reaction. 

d. What is the source of the energy developed by the current from 

the cell? 

122. a. What is meant by local action in a cell? 

b. How may it be prevented? 

c. What is meant by polarization in a cell? 

d. What is the effect of polarization? 

e. How may it be prevented by chemical means? 

123. a. State the principle involved in all depolarizers. 

b. What class of compounds are employed as depolarizers? 

c. Name three substances which may be used as depolarizers. 

d. Why are depolarizers employed? 

CHAPTER 20. 

124. a. Make a diagram of a Grove cell. Name and mark the materials 

employed. 

b. Write the chemical reactions which take place and indicate the 

parts of the cell in which these occur. 

c. How is polarization overcome? 

d. What are the disadvantages of this cell? 

125. a. Make a diagram of a Bunsen cell. Name and mark the mate- 

rials employed. 

b. Write the chemical reactions which take place and indicate the 

parts of the cell in which these occur. 

c. What advantage has this cell over the Grove cell? 

d. Why are the Bunsen, Grove and Daniell cells preferable to the 

simple voltaic cell? 



20 

126. a. Make a diagram of a Daniell cell. Name and mark the mate- 

rials employed. 

b. What is its average E. M. F.? 

c. Write the chemical reactions which take place and indicate the 

parts of the cell in which they occur. 

d. Does this cell develop any E. M. F. of polarization? 

e. For what is it generally used? 

127. a. Make a diagram of a gravity cell. Name and mark the mate- 

rials employed. 
b. Write chemical reactions which take place in the cell and indi- 
cate where these reactions occur. 

128. a. What is the positive plate in the Edison-Lalande cell? 

b. What is the electrolyte? To what deterioration is it liable? 

c. What depolarizer is used? 

d. Write chemical reactions which take place in this cell. 

e. What voltage does it produce? 

129. a. Make a diagram of a Leclanche cell. Name and mark the 

materials employed. 

b. What is its average E. M. F.? 

c. Write the chemical reactions which take place in the cell and 

indicate the parts in which they occur. 

d. What are the advantages and disadvantages of this cell? 

e. For what purpose is it most largely used? 

130. a. Make diagram of a section of a dry cell. 

b. Name and mark materials employed, explaining object of each. 

c. Write chemical reactions which take place in the cell. 

d. For what use is it best suited? 

131. a. Make diagram of a section of a Clark's cell. 

b. What is its E. M. F.? 

c. Name and mark materials employed, explaining object of each. 

d. For what is this cell used? 

CHAPTER 21. 

132. a. Write the reaction for the electrolysis of water. 

b. Indicate weight and volume relations. 

c. Find the weight of water to produce 10 cubic feet of oxygen at 

273° C and 15 lbs. pressure. 

133. A steady current through a water voltameter liberates in one hour 

.036 gram of hydrogen. Find the current. 



21 

134. A current of 3 amperes flows for 10 minutes through a dilute solu- 

tion of sulphuric acid. Find the weight of gas released. 

135. a. A steady current flowing through a gas voltameter for one hour 

liberates .072 gram of hydrogen. What is the current? 
b. Two such voltameters are connected in series and a current is 
sent through them for an hour. The total amount of hydro- 
gen liberated is as before .072 gram. What is the current? 

136. a. State Faraday's laws of electrolysis. 

b. Arrange three cells and a copper voltameter in series. Find 
the quantity of zinc consumed in the battery and the amount 
of copper deposited in the voltameter by a current of two 
amperes flowing for one minute. 

137. a. Make a diagram of an electrolytic cell containing CuS0 4 . In- 

dicate the direction of flow of current and name the terminals 
of the cell. 

b. Write reaction for the electrolysis of CuS0 4 and indicate what 

becomes of the products of electrolysis. 

c. Define the electro-chemical equivalent of hydrogen. 

138. a. What is the chemical equivalent of an element? What is the 

chemical equivalent of a radicle? 

b. How are the chemical equivalents found? 

c. What is the electro-chemical equivalent of hydrogen? 

d. What does this mean? 

e. How are the electro-chemical equivalents found? 

/. Give the chemical and the electro-chemical equivalents of Cu 7 

Zn, Ag and Pb. 
g. Define an ampere of current. 

139. A current through a copper voltameter deposits 2.36 grams of 

copper in one hour. Find the average value of the current. 

140. A cell supplies a steady current for one hour. At the end of this 

time the zinc plate is found to have lost in weight 2.43 grams. 
Find the current. 

141. A silver bowl is to be gold plated on the interior. The atomic 

weight of gold is 196 and its valency is 3. Its value is 66 
cents per gram. The current used is 5 amperes. How long 
should it flow in order that $3.00 worth of gold may be de 
posited on the bowl? 



22 



142. A Daniell cell furnishes a steady current for 30 minutes during which 

time 1.4625 grams of zinc are dissolved. Find the current. 

143. A Daniell cell delivers a steady current of 5 amperes for a certain 

time at the end of which the zinc plate is found to have 
lost in weight 75 grams. How long did the current flow? 

144. A battery of six cells in series supplies a steady current for one 

hour. At the end of this time 7.29 grams of zinc have been 
consumed. What was the current? 

145. Compare the amount of zinc consumed in each battery while 12 

grams of copper are being deposited in each voltameter. 




[-■H'l'r-b-®-! 



Fig. 2. 



146. Each battery is furnishing 2 amperes. How much zinc would be 
consumed in each in 5 minutes? 




<5h 



Fig. 3. 

147. Compare the amounts of zinc consumed in the batteries while 10 
grams of copper are being deposited in each voltameter. 



tin 



^H 



i<£r«h 



Fig. 4. 

148. Compare the amounts of zinc consumed in each battery while 12 
grams of copper are being deposited in each voltameter. 




I I III 



'h@n 



Fig. 5. 



23 



149. Each battery is sending a current of 5 amperes. How much zinc 
is consumed in each in 10 minutes? 



Illl 



<^ 




Fig. 6. 

CHAPTER 22. 

150. Enumerate and explain the phenomena relied upon as indications 

that a lead sulphuric-acid battery is charged. 

151. Enumerate and explain the principal uses of the storage battery. 

CHAPTER 24. 

152. The resistance of a reel of single conductor cable was measured 

and found to be 26.32 ohms. The diameter of the copper 
conductor was 0.102 inch. The resistance of one foot of 
copper wire .064 inch in diameter is .002521 ohm. Find 
the length of the cable on the reel. 

153. A submarine cable consisting of a number of insulated copper 

conductors is struck by the propeller of a vessel and severed. 
The diameter of a conductor is .081 inch. The resistance 
between the shore ends of two of the conductors is measured 
and found to be 8.374 ohms. A copper wire whose diameter 
is .051 inch has a resistance of .004009 ohm per foot. Find 
the distance from the shore end of the cable to the break. 

154. A wire cable between two distant supports sags of its own weight 

until it stretches one-tenth of its original length. How does 
its resistance compare with its original resistance? 

155. The resistance of a wire 50 meters long and .06 centimeter in diam- 

eter is 3 ohms. What is the specific resistance of the metal 
of which the wire is composed? What does this mean? 

156. The resistance of an iron wire 100 meters long and 3 millimeters 

in diameter is 1.7 ohms. Find the specific resistance of the 
iron. 

157. The specific resistance of mercury is 94.3 microhms. Calculate 

the resistance of a column of mercury 1 square millimeter 
in cross-section and 106.3 centimeters long. 



24 

158. The ohm is defined as the resistance at 0° C of a column of mercury 

106.3 centimeters in length and 1 square millimeter in cross- 
section. What is the specific resistance of mercury? What 
does this mean? 

159. A coil of wire between two points has a resistance of 112.5 ohms. 

Find the resistance that must be placed in parallel with the 
coil in order to reduce the resistance between the points to 
100 ohms. 

160. The resistance of a certain coil of wire is 10,000 ohms. On a damp 

day, the surface of the coil is coated with moisture and its 
measured resistance is only 9890 ohms. Find the resistance 
of the film of moisture. 

161. a. Two points, A and B, are joined by three coils of wire whose 

resistances are 3, 5 and 8 ohms respectively. What is the 
joint resistance between A and B1 
b. A fourth wire whose resistance is 1 ohm is added. What is 
now the resistance between A and Bt 

162. The joint resistance of three wires in parallel is 1/2 ohm. The 

resistance of one wire is 2 ohms, of another is 3 ohms. Find 
the resistance of the third. 

163. The resistance between two points on a wire is 5 ohms. Six ad- 

ditional pieces of equal-sized wire are strung between the 
two points and the total resistance is now found to be 2 
ohms. What is the resistance of each of the pieces of 
wire? 

164. A cube is outlined in wire. The resistance of the wire on each 

edge of the cube is 1 ohm. What is the total resistance from 
one corner of the cube to the diagonally opposite corner? 

165. Three points A, B and C, the vertices of an equilateral triangle, 

are connected by wires and a fourth wire connects the ver- 
tex A with the center of the opposite side. The resistance 
of each wire is 1 ohm. Find the resistance between A 
and C. 

166. A reel of insulated cable was found to have a resistance of 10.88 

ohms at a temperature of 75° F. The diameter of the copper 
core was one-tenth of an inch. If the resistance of a mil foot 
of copper at 75° F be taken as 10.505 ohms, what was the 
length of the cable? 



25 

167. a. The diameter of a No. 6 copper wire is 0.162 inch. Find its area 

in circular mils. 
b. The resistance of a mil foot of copper wire at 75° F is 10.505 
ohms. Find the resistance of one foot of the No. 6 wire at 
the same temperature. 

CHAPTER 25. 

168. The resistance between two points is 1/1000 of an ohm. The dif- 

ference of potential between the points is 1/500 of a volt. 
What current is flowing in the circuit? 

169. A storage battery whose E. M. F. is 110 volts and internal resist- 

ance is 0.5 ohm is to be charged by connecting it across mains 
between which there is a difference of potential of 240 volts. 
What resistance must be connected in series with the battery 
so that the charging current shall not exceed 15 amperes? 

170. The E. M. F. of a storage battery is 112 volts. Its internal resist- 

ance is 0.6 ohm. The normal charging current is 15 amperes. 
What voltage must be applied to the battery to produce this 
charging current? 

171. Five cells, each of an E. M. F. of 2 volts and an internal resistance 

of 1 ohm, are arranged in series, but through error two are 
faced in the wrong direction. What current will the battery 
send through an external resistance of 3 ohms? 

172. The specific resistance of German silver is 30 microhms. The 

diameter of a given piece of wire of this material is 2 milli- 
meters and its length is 3 meters. Find the difference of 
potential that must be established between the ends of this 
wire in order to drive through it a current of 2 amperes. 

173. Three lamps whose resistances are 250, 150 and 100 ohms respec- 

tively are connected in series between two leads whose 
difference of potential is 250 volts. Assuming the potential 
of the negative lead to be 10 volts, find the potentials of the 
terminals of the inner lamp. 

174. a. A battery whose E. M. F. is 105 volts and internal resistance 

1 ohm is sending a current over leads whose total resistance 
is 2 ohms and through 3 lamps in parallel. The resistance of 
each lamp is 201 ohms. Find the current through the circuit. 
6. Find the difference of potential between the terminals of the 
battery and across the terminals of the lamps. 



26 

175. a. Make a diagram of a divided circuit of three branches, each 

branch having a resistance of 150 ohms. Mark the extrem- 
ities of the divided circuit A and B respectively. What is 
the joint resistance between A and 5? 

b. If the difference of potential between A and B is 100 volts, what 

is the current in the main circuit? 

c. The resistance of the remainder of the circuit is 5 ohms; what 

is the total E. M. F. of the circuit? 

176. a. Make a diagram of a divided circuit of two branches having 

resistances of 5 and 3 ohms respectively. 
b. If the current in the main circuit be 5 amperes, what is the 
current in each branch? 

177. A circuit is in the shape of a rectangle, the resistance of each side 

being 3 ohms. A battery of an E. M. F. of 3 volts and an 
internal resistance of 1 ohm is connected in parallel with one 
of the sides. Find the currents in the different parts of the 
circuit. 

178. a. Make a diagram of a divided circuit of three branches of 3, 4 

and 5 ohms resistance respectively. 
b. If the current in the main circuit be 3 amperes, what is the 
current in each branch? 

179. A current of 15 amperes is flowing through a divided circuit of 3 wires 

in parallel, their respective resistances being 3, 4 and 5 ohms. 
Find the current in the wire whose resistance is 4 ohms. 

180. A current of 10 amperes is passed through resistances of 2, 7, 12 

and 30 ohms in parallel. Find the current in each branch 
and the drop of potential across the divided circuit. 

181. a. Two resistances of 5 and 8 ohms are connected in series. The 

difference of potential between the extremities of the 8 
ohms is 16 volts. What is the difference of potential be- 
tween the extremities of the 5 ohms? 
b. If these resistances be connected in parallel, what is the current 
through each when there is a difference of potential of 40 
volts between their extremities? 

182. a. The drop of potential between the extremities of a divided 

circuit of three branches is 10 volts. The resistance of two 
of these branches is 2 and 5 ohms respectively. The current 
in the main circuit is 10 amperes. What is the resistance of 
the third branch? 
b. What is the current in each branch? 



27 

183. A battery is connected in series with a resistance of 0.5 ohm and 

an ammeter whose resistance is 1 ohm. The ammeter in- 
dicates a current of 1.75 amperes. The ammeter is then 
shunted with a resistance of 0.25 ohm and its reading is re- 
duced to 0.49 ampere. Find the resistance of the battery. 

184. The resistance of each coil from a to b is 400 ohms; from c to d is 

80 ohms; from e to / is 16 ohms. Find the difference of poten 
tial between a and g when the current in the main circuit is 
4 amperes 

a H>wro / ^fjs<ni!i<p^ b 

c o^owoifir<>yrx2^^ d 

g 

Fig. 7. 

185. a. Make a diagram of a copper voltameter and a shunt. 

b. The resistance of the shunt is 1/9 of the resistance of the 
voltameter and its leads. In one hour 1.134 grams of copper 
are deposited in the voltameter. Find the current in the 
main circuit. 

186. a. Make a diagram of a copper voltameter and a shunt. 

b. The resistance of the shunt is 1/99 of the resistance of the 
voltameter and its leads. In one hour .567 gram of copper 
is deposited in the voltameter. Find the current in the 
main circuit. 

187. a. Make a diagram of a copper voltameter and a shunt. 

b. The resistance of the shunt is 1/999 of the resistance of the 
voltameter and its leads. In one hour .01134 gram of copper 
is deposited in the voltameter. Find the current in the 
main circuit. 

188. The resistance of a galvanometer is 200 ohms. Find the resistance 

of the shunt which will cause 1/25 of the total current in 
the circuit to flow through the galvanometer. 

189. a. A galvanometer whose resistance is 2572 ohms is shunted with 

a resistance of 285.8 ohms. What fraction of the total cur- 
rent flows through the galvanometer? 
b. Find the resistance of the shunt to be used with a galvanometer 
of 5461 ohms resistance so that 1/100 of the total current 
will flow through the galvanometer. 



28 

190. An electric circuit is in the shape of a circle across which is drawn a 

horizontal diameter. On the upper semicircle, whose resist- 
ance is 12 ohms, there is a battery of 10 volts faced to the right. 
On the diameter whose resistance is 6 ohms, there is a battery 
of 20 volts faced to the left. The resistance of the lower semi- 
circle is 20 ohms. Find the current in the three branches. 

191. An electric circuit is in the shape of a circle across which is drawn 

a horizontal diameter. On the upper semicircle, whose resist- 
ance is 8 ohms, there is a battery of 12 volts. On the diameter, 
whose resistance is 1 ohm, there is a battery of 4 volts. On 
the lower semicircle, whose resistance is 2 ohms, there is a 
battery of 6 volts. All three batteries face to the right. Find 
the current in each branch and the direction of its flow. 

192. a. A battery composed of two cells and of an E. M. F. of 4 volts 

and an internal resistance of 0.2 ohm is placed in one branch 
of a divided circuit, and a single cell of an E. M. F. of 2 volts 
and an internal resistance of 0.1 ohm is placed in the other, 
both facing to the right. Complete the circuit through an 
external resistance of 1 ohm. Find the current in the ex- 
ternal circuit. 
b. Find the current through the single cell. 

193. a. In problem 192, find what must be the resistance of the external 

circuit so that no current will flow through the single cell. 
b. Find the current through this resistance. 

194. A battery composed of two cells and of an E. M. F. of 4 volts and 

an internal resistance of 2 ohms is placed in one branch of a 
divided circuit, and a single cell of an E. M. F. of 2 volts 
and an internal resistance of 1 ohm is placed in the other, 
both facing to the right. Complete the circuit through an 
external resistance. Neglecting the resistance of the branches, 
find the current in the external circuit and in the branches 
when R = oo, R = l, R=0. 

195. A battery whose E. M. F. is 6 volts and internal resistance 0.3 

ohm is connected in series in a circuit in the shape of a circle 
with a second battery whose E. M. F. is 4 volts and internal 
resistance 0.2 ohm, the two batteries being on opposite sides 
of the circle. The resistance of the external circuit is 2 ohms. 
A wire whose resistance is 1 ohm is stretched diametrically 
across the circle and midway between the two batteries. 
Find the current in this wire. 



29 

196. Four horizontal parallel wires, A, B, C and D, are connected at 

their extremities. The resistance of A is 84 ohms, that of 
B is 42 ohms, that of C 6 ohms, that of D 24 ohms. A bat- 
tery on A faced to the left has an E. M. F. of 18 volts; a 
battery on B faced to the right has an E. M. F. of 12 volts; 
a battery on C faced to the right has an E. M. F. of 36 volts. 
Find the current in each branch and indicate the direction of 
its flow. 

197. The resistance of each side of a rectangle of wire is 1 ohm. A cell 

is connected between each pair of diagonally opposite corners 
of the rectangle. The E. M. F. of each cell is 1 volt and the 
resistance of each cell with its diagonal wire is 2 ohms. Find 
the current through each cell. 

198. Make a diagram of a rectangle and its two diagonals and suppose 

these six lines to represent wires, each of 1 ohm resistance. 
The diagonals are not connected at the point of crossing. 
A cell of an E. M. F. of 1 volt and of negligible internal 
resistance is inserted in the upper and a second one in the 
lower side of the rectangle, one faced to the right, the other 
faced to the left. Find the current through the cells. 

199. a. A battery whose internal resistance is 3 ohms is sending a cur- 

rent of 5 amperes through an external resistance of 10 ohms. 
Find the useful volts. 
b. Find the lost volts. 

200. A given cell has an E. M. F. of 2 volts and an internal resistance 

of 0.25 ohm. When it is delivering current through a cir- 
cuit, a voltmeter across its terminals reads one volt. What, 
is the resistance of the external circuit? 

201. When a certain battery is furnishing a current of 2 amperes, the 

difference of potential between its terminals is 12 volts. 
When the current is increased to 3 amperes, this drops to 
10.75 volts. Find the internal resistance of the battery. 

202. A battery of dry cells has an E. M. F. of 21 volts and an internal 

resistance of 4.5 ohms. It is connected in series with a resist- 
ance of 9.5 ohms. Find the voltage between its terminals. 

203. A battery whose internal resistance is 1 ohm is supplying a current 

of 4 amperes. The voltage across its terminals is 80. Find 
what this voltage becomes when the current is doubled. 



30 

204. A battery is composed of a number of Daniell cells in series, each 

of an E. M. F. of 1.07 volts. One of these having been dam- 
aged is taken out and in its place is inserted a dry cell whose 
E. M. F. is 1.4 volts and internal resistance 0.3 ohm. A 
current of 5 amperes is now drawn from the battery. Show 
whether the dry cell is a help or a hindrance. 

205. A cell whose E. M. F. is 2 volts and internal resistance is 0.2 ohm 

is connected in parallel with a cell whose E. M. F. is 1 volt 
and internal resistance 0.1 ohm. The wires connecting the 
terminals of the cells have each a resistance of 0.1 ohm. 
Find the difference of potential between the middle points 
of these wires. 



CHAPTER 26. 

206. a. Make a lozenge-shaped diagram of the Wheatstone bridge 

with battery and galvanometer connected and with keys in 
the circuits. 
b. If the resistance in the A arm be 100 ohms and that in the B 
arm be 1000 ohms, what is the resistance in the R arm when 
the bridge is balanced and X = 320 ohms? 

207. a. Complete the printed diagram of the Wheatstone bridge here- 

with by inserting the battery, the galvanometer and the un- 
known resistance and by arranging the wiring so that the 
switches will be in the proper circuits. 
b. Supposing the unknown resistance to be 37.54 ohms, mark with 
a cross the plugs to be removed in the three arms of the 
instrument to bring it to a balance. 



3 



JT /po o too /o i i io ioo a h 

O poooOooo 

-() / 2 3 4 10 20 30 40 

^ poooooooo 

^ — ' 4000 6000 2000 IOOO 40D 300 ZOO lOO 

q DQQQQOOQQ 




O 



< ) *g> 



^^> 



'<ey C h 



Fig. 8. 






31 

208. a. A difference of potential of one volt is maintained across the 

battery terminals of a Wheatstone bridge. In measuring to 
the nearest unit a resistance of 100 ohms, an error is made 
and a resistance of 101 ohms is unplugged in the R arm. 
Compare the difference of potential across the galvanometer 
when the 10-ohm coils are unplugged in the A and B arms with 
that when the 100-ohm coils are unplugged in these arms. 

b. In which case would the greater current flow through the 

galvanometer? 

c. In which case would the error made in the R arm be most 

apparent? 

209. A battery whose E. M. F. is 9.5 volts is connected in series with 

resistances of 6 and 12 ohms. A voltmeter connected across 
the 6 ohms reads 3 volts. What is the internal resistance 
of the battery? 

CHAPTER 27. 

210. A current is flowing in the direction AB along a fine wire whose 

resistance is one-tenth of an ohm per inch. The positive 
pole of a Clark's cell is connected to A. The negative pole 
is connected to a galvanometer and a wire C from the re- 
maining terminal of the galvanometer is slid along AB until 
the galvanometer needle shows no deflection. At this mo- 
ment, the distance from A to C is 23.9 inches. Find the 
current in AB. 

211. Through a wire AS of 0.239 ohm resistance a steady current is 

flowing from A to B. A Clark's cell with a galvanometer 
in series is shunted between A and B, the positive pole of 
the cell being connected to A. If the galvanometer indicates 
no current, find the current in AB. 

212. a. A battery of an E. M. F. of 2.14 volts and an internal resistance 

of 0.70 ohm is connected in a circuit composed of a fine wire 
AB, one meter long and of a resistance of 10 ohms. The 
current enters at A. The negative pole of an unknown cell 
is connected to B, and the positive pole is connected through 
a galvanometer to a movable contact which is slid along 
the wire AB. Make a diagram of the arrangement. 
b. When the movable contact is 72 cms. from B along the wire, 
the galvanometer indicates no current. Find the E. M. F. 
of the unknown cell. 



32 

CHAPTER 28. 

213. Eight cells, each of an E. M. F. of 2 volts and an internal resist- 

ance of 0.1 ohm, are connected in series with an external 
circuit whose resistance is 5.6 ohms. What is the difference 
of potential between the poles of any one of the cells? 

214. A circular circuit is arranged of six cells, each of an E. M. F. of 

2.5 volts and an internal resistance of 5 ohms, connected in 
series with a resistance of 120 ohms which is 30 inches long. 
Find the point on the circuit which if connected by a wire 
to the junction of the 1st and 2d cells there will be no cur- 
rent flow in the wire. 

215. a. A current through a gas voltameter liberates in one hour .072 

gram of hydrogen. What was the current? 
6. This current is produced by x cells in series. The E. M. F. of 
each cell is 3 volts, its resistance 1 ohm. The total external 
resistance is 5 ohms and the back E. M. F. of the voltameter 
is 2 volts. Find the number of cells. 

216. A battery of 16 dry cells is enclosed under the seat of an auto- 

mobile. It is thought that perhaps some of the cells are im- 
properly connected. Two similar cells are connected in series 
with the battery and send a current of 4 amperes through an 
ammeter. When these cells are reversed, the current drops 
to 3 amperes. What is the condition of the battery? 

217. Five cells are arranged in parallel. The E. M. F. of each cell is 

2 volts, its resistance 1 ohm and the external resistance is 3 
ohms. Find the current. 

218. A battery is composed of 36 cells grouped 9 in series and 4 in 

parallel. Compare the E. M. F. and resistance of the bat- 
tery with the E. M. F. and resistance of a single cell. 

219. a. Arrange 10 cells 5 in series, 2 in parallel. 

b. The E. M. F. of each cell is 1 volt, its internal resistance is 2 

ohms. Find the E. M. F. of the battery. 

c. Find the internal resistance of the battery. 

d. What current will the battery produce if its terminals be short 

circuited? 

220. Twelve cells are arranged 4 in series and 3 in parallel and a 

voltameter is inserted in the external circuit. How much 
zinc is consumed in the battery while 5 grams of copper are 
deposited in the voltameter? 



33 

221. Fifteen cells are grouped 3 in parallel, 5 in series, and a voltameter 

is inserted in the external circuit. Find the amount of zinc 
consumed in the battery while 10 grams of copper are de- 
posited in the voltameter. 

222. Ten cells are arranged in series. Ten others are arranged 2 in 

series, 5 in parallel. Each battery is then connected to a 
circuit containing a voltameter. Find the amounts of zinc 
consumed in the batteries while 5 grams of copper are de- 
posited in each voltameter. 

223. Eight cells are arranged in series. Eight others are arranged 2 in 

series, 4 in parallel. Each battery is then connected to a cir- 
cuit containing a voltameter. Find the amounts of zinc con- 
sumed in the batteries while 15 grams of copper are deposited 
in each voltameter. 

224. a. A battery of 8 cells is grouped 4 in series, 2 in parallel and con- 

nected in series with a divided circuit of three branches of 
equal resistance. In a voltameter placed in one of these 
branches, .036 gram of hydrogen is released in one hour. 
The E. M. F. of each cell is 2 volts and its internal resistance 
is 1 ohm. Find the total external resistance. 
b. Find the total current. 

225. A battery of 12 cells grouped 6 in series, 2 in parallel, is connected 

in circuit with a voltameter. The E. M. F. of each cell is 
2 volts, its internal resistance is 0.2 ohm. The resistance of 
the voltameter is 2.4 ohms and the resistance of the re- 
mainder of the external circuit is 3 ohms. Find the amount 
of copper deposited and of zinc consumed in 5 minutes. 

226. A battery consists of x cells in series, 2 in parallel. The E. M. F. 

of each cell is 2 volts, its internal resistance is 1 ohm. The 
battery is connected to a circuit whose resistance is 5 ohms. 
A voltameter with a back E. M. F. of 2 volts is inserted in 
this circuit. The current flows steadily for one hour, at the 
end of which time 0.108 gram of hydrogen has been released. 
Find the number of cells in the battery. 

227. A battery of 8 cells, grouped 4 in series, 2 in parallel, is connected 

in series with a divided circuit of three branches whose re- 
sistances are 2, 3 and 4 ohms respectively. The E. M. F. of 
each cell is 2 volts, its internal resistance is 1 ohm. Find the 
current in the 3-ohm branch of the divided circuit. 



34 

228. Twelve cells are arranged (a) 4 in series, 3 in parallel, (b) 3 in 

series, 4 in parallel. The E. M. F. of each cell is 1 volt, its 
internal resistance is 2 ohms and the resistance of the ex- 
ternal circuit is 15 ohms. Find the current for each com- 
bination. 

229. Twelve cells are arranged (a) 4 in series, 3 in parallel, (b) 3 in 

series, 4 in parallel. The E. M. F. of each cell is 2 volts, 
its internal resistance 0.3 ohm. The external circuit has a 
resistance of 6 ohms and contains a voltameter which exerts 
a back E. M. F. of 1.5 volts. Find the current for each 
combination. 

230. Given 20 Daniell cells, each of an E. M. F. of 1.07 volts and an 

internal resistance of 1 ohm. Find the maximum current that 
they can send through a resistance of 0.85 ohm. 

231. a. Given 8 cells, each of an E. M. F. of 1 volt and an internal 

resistance of 2 ohms; arrange these cells to send a maximum 
current through a circuit consisting of two branches, each 
of a resistance of 2 ohms. 
b. What is this current? 

232. a. Given 12 cells, each of an E. M. F. of 1 volt and an internal 

resistance of 4/13 ohm; arrange these to send a maximum 
current through a divided circuit of three branches whose 
resistances are 2, 3 and 4 ohms, respectively. 

b. What is the current? 

c. What is the current through the branch of 2 ohms resistance? 

233. a. Given 16 cells, each of an E. M. F. of 1 volt and a resistance 

of 3.2 ohms. How must these be arranged to send a maxi- 
mum current through a circuit composed of three branches 
of 4, 2 and 2 ohms resistance, respectively? 

b. What is the current in the branch whose resistance is 4 

ohms? 

c. How much zinc will be consumed in the battery in 1 hour? 

234. a. A current through a copper voltameter deposits 3.39 grams of 

copper in 1 hour. Find the current. 
6. This current is produced by a battery of s cells in series and p 
in parallel arranged to send maximum current. The E. M. F. 
of each cell is 2 volts, its internal resistance 1 ohm. The total 
external resistance is 5 ohms. Find the number of cells in 
the battery. 



35 

235. a. Arrange 6 cells in series, completing circuit and indicating by 

arrowheads direction of the current. 

b. Without disturbing the position of these cells, change wiring 

so that they are all in parallel. 

c. Wire them 3 in series, 2 in parallel. 

d. Wire them 2 in series, 3 in parallel. 

236. a. Arrange 8 cells in series, completing the circuit and indicating 

by arrowheads direction of the current. 

b. Without disturbing position of these cells, change wiring so 

that they are all in parallel. 

c. Wire them 4 in series, 2 in parallel. 

d. Wire them 2 in series, 4 in parallel. 

237. a. Arrange 10 cells in series, completing the circuit and indicating 

by arrowheads direction of the current. 

b. Without disturbing position of these cells, change wiring so 

that they are all in parallel. 

c. Wire them 5 in series, 2 in parallel. 

d. Wire them 2 in series, 5 in parallel. 

238. a. Arrange 9 cells in series, completing circuit and indicating by 

arrowheads direction of the current. 
6. Without disturbing the position of these cells, connect them all 
in parallel. 

c. Connect them 3 in series, 3 in parallel. 

d. The E. M. F. of each cell is 1 volt, the resistance of each is 2 

ohms. Find the E. M. F. of each combination. 

e. If the poles of the battery be short circuited, find the current 

for each combination. 

239. a. Arrange 6 cells in series. 

b. Without disturbing the position of these cells, connect them all 

in parallel. 

c. Connect them 3 in series, 2 in parallel. 

d. The E. M. F. of each cell is 1 volt. Find the E. M. F. of each 

of the above combinations. 

e. The internal resistance of each cell is 0.5 ohm. Find the cur- 

rent that each of the above combinations will send through 
an external resistance of 10 ohms. 



36 

240. a. Arrange 15 cells in series. 

b. Without disturbing the position of these cells, connect them all 

in parallel. 

c. Connect them 5 in series, 3 in parallel. 

d. The E. M. F. of each cell is 2 volts. Find the E. M. F. of each 

of the above combinations. 

e. The internal resistance of each cell is 1 ohm. What current 

will the above combinations send through an external re- 
sistance of 2 ohms? 

CHAPTER 29. 

241. A telegraph wire runs east and west. Explain how by means of a 

magnetic needle you may determine whether a current is 
flowing in the wire or not, and if so, in what direction. 

242. a. Make two dots a convenient distance apart. Letter one A, 

the other N. A represents the cross-section of a wire carry- 
ing a current going in to the paper. Draw a line of force due 
to this current. What is the positive direction of the lines 
produced by this current? 

b. N represents a free north pole. Draw the action line of the 

force acting upon N. 

c. Give clock rule for determining from direction of the flow of the 

current the positive direction of the resulting field. 

243. a. Make two dots a convenient distance apart. Letter one A, the 

other N. A represents the cross-section of a wire carrying 
a current coming out from the paper. Draw a line of force 
. due to this current. What is the positive direction of the 
lines produced by this current? 

b. N represents a free north pole. Draw the action line of the 

force acting upon N. 

c. Give clock rule for determining from the direction of the flow 

of the current the positive direction of the resulting field. 

244. a. Make two dots a convenient distance apart. Letter one A, the 

other S. A represents the cross-section of a wire carrying a 
current going in. S represents a free south pole. Draw a 
line of force due to the current and mark its positive direction. 

b. Give clock rule for determining the positive direction of the 

field about a conductor carrying a current. 

c. Draw action line of force acting on S. 






37 

245. a. Make two dots a convenient distance apart. Letter one A, the 

other S. A represents the cross-section of a wire carrying a 
current coming out. S represents a free south pole. Draw a 
line of force due to the current and mark its positive direction. 

b. Give rule for determining the positive direction of the field 

about a conductor carrying a current. 

c. Draw action line of the force acting upon S. 

246. a. AB represents the cross-section of a coil placed in the mag- 

netic field produced by the poles NS. If a current flows in 
at A and out at B, in which direction will the coil move? 




Fig. 9. 
b. Give the left-hand rule for determining this direction. 

a. A current of one absolute unit is flowing from right to left in a 

horizontal straight wire. With what force will it act upon a 
free south pole of 3 units strength placed vertically above the 
wire and at a distance of 5 cms.? 

b. In what direction will the pole be urged? 

c. Give rule for determining this direction. 

a. A current of 10 amperes is flowing from top to bottom of a 

straight vertical wire. A free north pole of 5 units strength 
is placed at a distance of 10 cms. to the right of the wire. 
With what force is it acted upon? 

b. In what direction will it be urged? 

c. Give rule for determining this direction. 

A circular coil consisting of 50 turns of an average diameter of 25 
cms. is carrying a current of 1.25 amperes. Find the force 
with which a pole of strength 3 will be acted upon when 
placed at the center of the coil. 

a. With what force will a current of 3 absolute units flowing in a 
circular coil of 20 cms. radius and 30 turns act upon a unit 
pole placed at the center of the coil? 

6. How many amperes are flowing in the coil? 

c. Define the absolute unit of current. 



38 

251. a. Make a diagram of a circular coil carrying a current flowing 

counter clockwise. If the current be 2 absolute units, the 

radius of the coil be 10 cms. and the number of turns be 50, 

find the field at the center. 
6. Indicate the direction in which a free north pole at the center 

would move. 
c. Give rule for determining this direction. 

252. a. With what force will a current of 5 amperes flowing in a cir- 

cular coil of 5 cms. radius and 10 turns act upon a pole of 3 
units strength placed at the center of the coil? 

b. How many absolute units are flowing in the coil? 

c. Define the absolute unit of current. 

253. a. What field is produced at the center of a coil of 4 cms. radius 

and 10 turns by a current of 3 amperes? 

b. With what force will this field act upon a magnetic pole of 5 

units strength? 

c. Define the absolute unit of current. 

254. A wire 30 cms. in length and carrying a current of 10 amperes lies 

at right angles to a magnetic field of 400 lines of force per 
sq. cm. Find the force upon the wire. 

255. a. Deduce the general expression for the work done by a conductor 

carrying a current of I amperes and moving across a uniform 
magnetic field. 
b. Represent the field and the wire with its field and indicate the 
direction in which the wire would tend to move. 

256. a. A wire 50 cms. long lies at right angles to a magnetic field of 

2000 lines per sq. cm. While a current of 10 amperes is sent 
through the wire, the wire moves at right angles across the 
field through a distance of 100 cms. Find the work done by 
the current. 
b. Make a diagram of the magnetic field and of the field due to the 
current and indicate the direction in which the wire moves. 

257. a. A wire 50 cms. long lies at right angles to a uniform magnetic 

field. A current of 10 amperes is sent through the wire 
causing it to move 100 cms. at right angles to the field and 
to perform 10,000,000 ergs of work. Find the intensity of 
the field. 
b. Make a diagram of the field due to the magnet and to the cur- 
rent and indicate the direction of motion of the wire. 



39 

258. a. Make cross-sections of two parallel wires and indicate the posi- 

tive direction of the fields due to currents flowing in in each. 

b. In what direction will the wires tend to move? 

c. Make cross-sections of two parallel wires and indicate the 

positive direction of the fields due to currents flowing in in 
one and out in the other. 

d. In what direction will the wires tend to move? 

CHAPTER 30. 

259. a. Make a diagram of the multiplier, indicating the positive 

direction of the current. 

b. State the principle involved in its use. 

c. Mark the poles of a magnetic needle suspended within the coil 

and indicate the direction in which the north pole will move. 

d. If the number of turns in the coil be increased, what will be 

the effect upon the deflection of the needle? 

260. a. Make a diagram of Hauy's method of neutralizing the directive 

force of the earth's magnetism. 

b. What is the object of this neutralization? 

c. Make a second diagram showing the compensating magnet 

nearer to the magnetic needle than necessary for neutraliza- 
tion. What results? 

261. A supposedly astatic pair of needles is suspended from the vertical 

wire of a torsion balance. When the torsion head is twisted 
through an angle of 75°, the needles are deflected 30° from 
the meridian. One of the needles is now reversed end for 
end and in order to make the pair stand at right angles to 
the meridian the torsion head must be turned through 360°. 
Find the relative strength of the poles of the two needles. 

262. a. Make a diagram of a perfect astatic pair suspended in a mag- 

netic field by a fine metallic thread. What determines the 
position that the pair will assume? 

b. Make a diagram of a wire passing below the lower needle, thence 

between the needles, and then above the upper needle. 
Mark the assumed direction of the current in the wire and 
indicate the effect upon the astatic pair. 

c. What is the controlling force and what the deflecting force? 

d. How may the deflecting force be increased? 



40 

263. a. You are facing a circular coil in which a current is flowing clock- 

wise. Which is the south face of the coil? 

b. What is the positive direction of the lines of force within the 

coil? 

c. In what direction would a free south pole move along these lines? 

264. a. Represent the cross-section of a circular coil in a vertical plane. 

A current is flowing in at the top and out at the bottom. A 
bar magnet is placed along the axis of the coil, its center in 
the plane of the coil, its north pole to the left. Construct the 
action lines in the plane of the paper of the forces upon the 
magnetic poles. 
b. Is the magnet in a position of stable of or unstable equilibrium? 
Why? 

265. a. Represent the cross-section of a circular coil in a vertical plane. 

A current is flowing in at the top and out at the bottom. 
A bar magnet is placed along the axis of the coil, its center 
in the plane of the coil, its north pole to the right. Con- 
struct the action lines in the plane of the paper of the forces 
upon the magnetic poles. 
b. Is the magnet in a position of stable or of unstable equilibrium? 
Why? 

266. a. State Maxwell's law. 

b. Show the application of this law to the case given in problem 
246. 

267. a. Represent the horizontal projection of a circular coil in the 

magnetic meridian with a magnetic needle suspended at its 
center. A current through the coil causes a deflection of x° 
in the needle. Represent the controlling and the deflecting 
forces and their active components. 

b. Equate the expressions for these components and solve for 

value of the deflecting field. 

c. How may we compare two currents by means of this instru- 

ment? 

d. Give name of instrument. 

268. The coil of a tangent galvanometer consists of 10 turns and is 1 

meter in diameter. It is set up at a locality where the hori- 
zontal component of the earth's magnetism is 0.19. A current 
sent through the coil produces a deflection of 45° in the needle. 
Find the current in amperes. 



41 

269. A tangent galvanometer whose coil consists of 5 turns of an average 

radius of 15 centimeters is set up in Washington where the hori- 
zontal component of the earth's magnetism is 0.2. Find the 
deflection produced in the needle by a current of 0.25 amperes. 

270. A tangent galvanometer whose coil consists of 5 turns of an aver- 

age radius of 12 centimeters is set up at Washington where 
the horizontal component of the earth's magnetism is 0.2. 
Find the current in amperes that must be sent through the 
coil in order to produce a deflection of 45° in the needle. 

271. Find the current in amperes that must be passed through a cir- 

cular coil of 72 turns of an average diameter of 20 centimeters, 
the plane of the coil being in the magnetic meridian, in order 
to produce a deflection of 45° in a small magnetic needle at 
the center of the coil. H = 0.2. 

272. A tangent galvanometer in a circuit whose total resistance is 800 

ohms shows a deflection of 30°. The resistance of the cir- 
cuit is altered and the galvanometer now shows a deflection 
of 10°. Find the change made in the resistance of the circuit. 

273. Two tangent galvanometers, A and B, are connected in series. 

Each has the same number of turns but the radius of the coil 
of A is three times the radius of that of B. A current causes 
the needle of A to be deflected 30°. Find the deflection of 
the needle of B. 

274. The coil of a given tangent galvanometer has a mean radius of 

20 cms. but is so wrapped with insulation that the number of 
turns can not be determined by examination. It is connected 
in series with a copper voltameter and the current is turned 
on. The needle of the galvanometer is deflected through an 
angle of 45°. The horizontal component of the earth's 
magnetism at the locality is 0.20. At the end of 30 minutes, 
.072 gram of copper has been deposited in the voltameter. 
Find the number of turns of the coil. 

275. A tangent galvanometer whose coil consists of 50 turns of an 

average radius of 25 cms. is set up at a certain locality and 
connected in series with a silver voltameter. A current 
flows through the circuit for a certain time during which the 
needle marks constantly a deflection of 45°. The cathode 
of the voltameter being weighed, the current was found by 
calculation to have been 0.1433 ampere. Find the horizontal 
component of the earth's magnetism at the given locality. 



42 

276. A tangent galvanometer whose coil consists of 5 turns is to be 

used at Washington, D. C, where the horizontal component 
of the earth's magnetism is 0.20. Find what must be the 
radius of the coil so that the natural tangents of the angles 
of deflection will read amperes direct, i. e., so that the in- 
strument may be used as an ammeter. 

277. A tangent galvanometer is set up with the plane of its coil at right 

angles to the magnetic meridian. A current is sent through 
the coil. The needle, caused to oscillate, makes 5 vibrations 
per minute. The current is reversed and the needle now 
makes 3 vibrations per minute. Compare the field pro- 
duced at the center of the coil by the current with the hori- 
zontal component of the earth's magnetism. 

278. a. A current through a sine galvanometer produces a deflection 

of 12°. Another current through the same instrument 
produces a deflection of 18°. Compare the deflecting 
fields. 

b. 1 = 1 ampere, radius of the coil = 20 cms., number of turns = 50. 

Find the field at the center of the coil. 

c. With what force will this field act on 2 units of magnetism 

placed at the center? 

279. What is the maximum current that can be measured at Washing- 

ton, D. C, by a sine galvanometer whose coil has 50 turns 
of an average radius of 20 cms., the horizontal component of 
the earth's magnetism at that locality being 0.20? 

280. a. Make a diagram of the d' Arson val suspended coil galvanometer 

and mark and name the parts. 

b. Indicate the field due to the magnets and show the positive 

direction. 

c. Indicate direction of current and positive direction of its field. 

d. Indicate direction of movement of coil. 

e. State why it will move. 

281. a. What is the controlling force and what the deflecting force in 

the suspended coil galvanometer? 
b. The coil of a tangent galvanometer consists of 50 turns of a 
diameter of 20 cms. The horizontal component of the earth's 
magnetism at the locality is 0.20. Find the current that 
must be sent through the instrument in order to produce a 
deflection of 45°. 



43 

282. a. At the extremities of an enlarged sign of addition (plus mark) 

make dots. Let these represent the cross-section by a hori- 
zontal plane of the two coils of an electro-dynamometer. 
The up and down line represents the fixed coil, the current 
flowing in at the upper dot. The horizontal line represents 
the movable coil, the current flowing in at the right-hand 
dot. Indicate the direction of the field of each coil. 

b. Indicate the direction in which the movable coil will turn. 

c. Reverse the current in both coils and indicate the direction in 

which the movable coil will now turn. 

d. Explain whether the instrument could be used with alternating 

currents or not. 

283. When a current of 3 amperes is passed through a Siemen's electro- 

dynamometer, the torsion head has to be turned through 225 
divisions of the scale in order to bring the pointer back to zero. 
When an unknown current is passed through the same instru- 
ment, the torsion head has to be turned through 169 divisions 
to bring the pointer to zero. Find the unknown current. 

284. a. When a current of 2 amperes is passed through a Siemen's 

electro-dynamometer, the torsion head has to be turned 
through 121 divisions of the scale in order to bring the pointer 
to zero. Find the constant of the instrument. 
b. If the current is increased to 2.18 amperes, through how many 
divisions must the torsion head be turned to bring the 
pointer back to zero? 

285. a. Make a diagram showing a gas voltameter and an electro- 

dynamometer connected in circuit for the purpose of finding 
the constant of the dynamometer. 
b. One coulomb flowing through a gas voltameter liberates 0.1738 
cc. of mixed gases at 0° C and 15 lbs. pressure. A current 
which gave a reading of 100 points on the dynamometer 
flowed for two minutes and liberated 16 cc. of gas. The 
temperature was 18° C, the pressure 15 lbs. Find the dyna- 
mometer constant. 

CHAPTER 31. 

286. a. Make a diagram of a solenoid wrapped upon a core. Mark the 

direction of the current. 

b. Indicate the direction of the field within the solenoid and give 

right-hand rule for determining same. 

c. Draw a complete line of force, marking its positive direction. 



44 

287. a. Represent diagrammatically a solenoid of 100 turns, 50 cms. 

long. 

b. Indicate the direction of the current and mark the poles of the 

solenoid. 

c. The current is 3 amperes. Find the field at the center. 

288. a. Represent diagrammatically a solenoid of 60 turns, 1000 cms. 

long. 

b. Indicate the direction of the current and mark the poles of the 

solenoid. 

c. The current is 2 amperes. Find the field at the center. 

289. a. Find the field at the center of a circular coil of 10 turns and 10 

cms. radius when the current is 5 amperes. 
6. Find the field at the center of a solenoid of 100 turns, 1000 cms. 
long, when it is carrying a current of 5 amperes. 

290. A solenoid 100 cms. long is wrapped with 3 layers of wire of 200 

turns each. Find the field at the center when a current of 5 
amperes is sent through the wire. 

291. a. A current of 1 ampere is flowing in a circular coil of 200 turns 

of a radius of 10 cms. Find the field at the center. 
b. Without changing the current, the coil is pulled out into a 
solenoid 50 cms. long. What is now the field at the center? 

292. A bar of iron is subjected to a magneto-motive force which would 

produce in air 20 lines of force per sq. cm. The permeability 
of the iron is 300. How many lines per sq. cm. radiate from 
the end of the bar? 

293. A bar of cast iron, 1 sq. cm. in cross-section, whose permeability 

is 833, is placed along the axis of a circular coil of 50 turns 
and 2 cms. radius. Find the current in amperes that must 
be sent through the coil in order to produce a flux of 15,000 
lines through the bar. 

294. a. The magnetizing force H applied to a specimen of soft iron 

was increased by steps from to 13, then decreased to — 13, 
then increased to 5 and the corresponding flux per sq. cm. 
was obtained in each case. The results of this experiment 
are given in the following table. Plot these results upon 
rectangular axes, the ordinates to a scale of one-quarter inch 
per 1000 lines of force and the abscissae one-quarter inch 
per unit. (See next page.) 



45 

294. b. Explain what is meant by coercive force and indicate upon the 
diagram the representation of this force. 

H B H B H B 









2 


12,500 


-6 


-13,000 


1 


1,000 





11,000 


-2 


-12,000 


2 


6,000 


- 1 


8,000 





-11,000 


4 


10,000 


- 2 





1 


- 7,000 


7 


12,100 


- 3 


- 7,000 


2 





13 


13,100 


- 7 


-12,000 


3 


7,000 



6 13,000 -13 -13,000 5 10,800 

295. a. Upon rectangular axes make a diagram of a hysteresis curve 

for one complete cycle. Cut this curve by two lines parallel 
to the axis of X and near together. Shade the area included 
between these lines, the axis of Y and the ascending branch 
of the curve. 

b. To what is the base of this little quadrilateral proportional? 

c. To what is its altitude proportional? 

d. To what is its area proportional? 

e. To what is the area of the entire curve proportional? 

296. A bar of soft iron 50 cms. in length and 9 sq. cms. in cross-section 

is magnetized to such a degree that /z = 320. Find the 
reluctance. 

297. a. Make a diagram of a solenoid of 50 turns, 100 cms. in length 

and 5 cms. radius, carrying 20 amperes. 

b. Find the magneto-motive force. 

c. Find the field at the center. 

d. Find the total flux. 

298. An iron rod whose length is 50 cms. and whose cross-section is 5 

sq. cms. is bent into the shape of a ring leaving a gap of 2 cms. 
between the ends. It is then wrapped with a coil of 2000 
turns. If the permeability of the iron be 2000, find the cur- 
rent that must be sent through the coil to produce a flux of 
25,000 lines across the gap. 

299. A circular iron ring whose mean radius is 15 cms. has cut from it 

a piece leaving a gap of 1 cm. The area of the cross-section is 
4 sq. cms. The remainder of the ring is wrapped with a coil 
of 1000 turns. If the permeability of the iron be 1500, find 
the flux across the gap when a current of 3 amperes is sent 
through the coil. 



46 

300. The magnetic circuit of a dynamo consists of the following parts: 

a cast iron portion 50 cms. long and 150 sq. cms. in cross- 
section, permeability 100; a wrought iron portion, 150 cms. 
long and 200 sq. cms. in cross-section, permeability 1000; an 
air gap, 1 cm. long and 200 sq. cms. in cross-section. Find 
the ampere turns to produce a flux of 1,000,000 lines of force 
in the circuit. 

301. An iron rod whose length is 100 cms. and whose cross-section is 2 

sq. cms. is bent into the shape of a ring leaving a gap of 3 cms. 
between the ends. If the permeability of the iron be 2000, 
find the total reluctance of the magnetic circuit. 

CHAPTER 32. 

302. The pole of a bar magnet whose cross-section is 2 sq. cms. having 

been placed against a block of soft iron, a force of 16ir dynes 
is required to separate the two. Find the flux per sq. cm. 
from the pole of the magnet. 

303. An electro-magnet, the cross-section of whose pole is 4 sq. cms. 

exerts a pull upon its armature of 25 lbs. Given 1 lb = 445,000 
dynes, find the flux per sq. cm. from the pole of the magnet. 

304. The flux from the pole of an electro-magnet of 3 sq. cms. cross- 

section is 10,000 lines per sq. cm. What pull in pounds will 
this magnet exert upon its armature? 1 lb = 445,000 dynes. 

305. a. Make a diagram of a battery connected to operate an electric 

bell by three independent push buttons. 

b. Make a diagram of a battery connected to operate three bells, 

each from an independent push button. 

c. Make a diagram of a battery connected to operate three bells 

simultaneously from one push button. 



CHAPTER 33. 

306. a. In the figure of problem 314, draw a line of force from the 
magnet and passing through the coil. 

b. The magnet is approaching the coil. Indicate the direction of 

the induced E. M. F. 

c. Give rule for determining this direction. 



N 



47 

307. a. A represents the cross-section of a wire carrying a current flow- 
ing in. Draw lines of force due to the poles and to 
the current. 

b. In which direction will the wire move? 
Fig. 10. " c - * n wnat direction is the E. M. F. induced by 

this motion? 
d. Give the rule for determining this direction. 

308. a. In the figure of problem 307, A represents the cross-section of a 

wire carrying a current flowing in. Draw lines of force due 

to the poles and to the current. 
6. The wire is moved up. In what direction will the induced 

E. M. F. be with respect to the original current? 
c. Give the general expression for the amount of work done by 

moving the wire across the field. 

309. a. In the figure of problem 307, A represents the cross-section of 

a wire carrying a current flowing out. Draw lines of force 
due to the poles and to the current. 

b. The wire is moved up. In what direction will the induced 

E. M. F. be with respect to the original current? 

c. Give rule for determining direction of this E. M. F. 

310. a. In the figure of problem 307, A represents the cross-section of 

a wire carrying a current flowing out. Draw lines of force 
due to the poles and to the current. 

b. In what direction will the wire move? 

c. In what direction is the E. M. F. induced by this movement? 

d. Give the rule for determining this direction. 

311. a. A wire perpendicular to the plane of the paper is moved across 

the magnetic field. Make a diagram 
of a hand placed so as to determine 

the direction of the induced E. M. F. 

b. Is this E. M. F. away from or towards 

________ the observer? 

c. Draw a line of force due to the induced 



Fig. 11. current. 

a. In the preceding problem suppose the wire to be moved down 
across the magnetic field. Make a diagram of a hand placed 
so as to determine the direction of the induced E. M. F. 

6. Is this E. M. F. away from or towards the observer? 

c. Draw a line of force due to the induced current. 



48 



O A 



Fig. 12. 



313. a. A and A' are cross-sections of a coil in a magnetic field which 

^ increases in intensity as we ascend. The 

\ coil is moving upward. Make a diagram 

of a hand so placed as to indicate the 
direction of the E. M. F. induced in A 
and in A' . 
b. What is the direction of the resultant 
E. M. F. in the coil? 

c. Give clock rule for determining this direction. 

d. Draw a line of force due to the induced current. Is it opposed 

to or in conjunction with the original field? 

314. a. Draw a line of force from the magnet and passing through the 

coil. 

b. The magnet is receding. Indicate 
the direction of the E. M. F. in- 
duced in the coil. 

c. Give rule for determining this di- 
rection. 

and if the lines of force embraced 




N 



Fig. 13. 

d. If the coil has 30 turns 

be reduced in one-tenth of a second from 10,000,000 to zero; 
find the induced E. M. F. in volts. 

315. a. Indicate the direction of the E. M. F. induced in A by closing 

the key in B. 
The coil A consists of 50 turns and 
when the current is flowing in B 
is penetrated by 1,000,000 lines 
of force. When the key is opened, 
the current in B is reduced to 
What is the E. M. F. in 





Fig. 14. 
zero in one-hundredth of a second, 
volts induced in A and what is the direction of this E. M. F.? 



316. a. The battery B is sending a current through the coil P which is 

wrapped about the iron ring. 
Draw a line of force due to 
this current. 

b. Indicate the direction of the 
E. M. F. induced in S by start- 
ing the current in P. 

c. If the current is sending 10 8 lines of 
force through the coil S, which has 100 turns, find the E. M. F. 
induced in S by reducing the current to zero in 1/60 of a second. 

d. What is the direction of this E. M. F.? 




49 

317. a. A rectangular coil of wire is suspended by a silk thread midway 

between two opposite magnetic poles, the north pole being 
at the left. By twisting the thread the coil, viewed from 
above, is caused to rotate in a clockwise direction. What is 
the direction of the induced E. M. F. and current in the coil 
at the instant when its plane is parallel to the line joining 
the poles? 

6. Apply the left-hand rule for determining the direction of motion 
of a conductor carrying a current and show in which direc- 
tion the coil is urged. 

c. State Lenz's law. 

318. a. Make a diagram of a ring transformer, lettering the primary 

coil P, the secondary coil S, and representing a battery in 
the primary circuit. Both circuits are closed. 

b. Indicate the direction of the current induced in S by starting 

the current in P. 

c. Draw a line of force due to this induced current. Is it opposed 

to or in conjunction with the field which produced it? 

319. a. Make a diagram of a ring transformer, indicating the direction 

of the current in the primary circuit. 

b. Draw a line of force due to this current. 

c. Indicate the direction of the E. M. F. induced in the secondary 

by decreasing the current in the primary. 

d. Compare the E. M. F. in the primary and secondary circuits. 

e. For what are transformers used? 

320. a. Make a diagram of a ring transformer, lettering the primary 

coil P, the secondary coil S, and representing a battery in 
the primary circuit. 

b. Draw a line of force due to the current in P. 

c. Indicate the direction of the E. M. F. induced in S by breaking 

the circuit in P. 

d. If 50,000 lines of force pass through S and if there are 2000 

turns in S, what E. M. F. is induced in S by reducing the 
current in P to zero in one second? 

e. What is the relation between the E. M. F. in P and in 5? 

321. a. Make a diagram of a ring transformer, naming the substance 

of which the ring is composed. 
b. Indicate the direction of the current in the primary circuit and 
draw a line of force due to this current. (Over J 



50 

321. c. Place an eye looking in the positive direction of this line of 

force and indicate the direction of the induced current in the 
secondary due to increasing the current in the primary. 
d. The E. M. F. in the primary is 5 volts, the number of turns 50, 
the number of turns in the secondary is 500; find the E. M. F. 
in the secondary. 

322. a. Why will an E. M. F. be induced in a coil carrying a current 

if the circuit be broken? 

b. What is the direction of this E. M. F. as compared with that 

of the original current? 

c. If an iron core be inserted in the coil before the circuit is broken, 

what effect will this have upon the induced E. M. F.? 

323. a. Represent by two dots in a vertical line the cross-section of a 

coil, the current flowing in at the upper dot. Indicate the 
direction of the field due to the current. 

b. What is the direction of the E. M. F. induced by starting the 

current in the coil? 

c. What is this phenomenon called? 

d. How would this E. M. F. have been affected had the coil en- 

closed an iron core? Why? 

324. Find the inductance in henrys of a cylindrical coil 30 cms. long, 4 

cms. in diameter and of 200 turns. 

325. An E. M. F. of 220 volts is applied to a circuit having a resistance 

of 6 ohms and an inductance of .05 henry. Find the current 
.005 of a second later. 

326. The coil of a large electro-magnet has a resistance of 50 ohms and 

an inductance of 20 henrys. If an E. M. F. of 200 volts be 
applied to the coil, how long will it be before the current 
rises to 3 amperes? • 

327. With the current flowing through the primary of an induction 

coil, there are 150,000 lines through the core. When the 
interrupter breaks the current in the primary, this flux is 
reduced to 10,000 in 1/500 of a second. There are 100,000 
turns in the secondary. What is the average E. M. F. in the 
secondary while the flux is decreasing? 



51 



Upon the diagram of the induction coil herewith, indicate by 

arrowheads the direction of the flow of the current in the 

primary at make. 
Draw a complete line of force due to this current. 
Indicate the direction of the E. M. F. induced in the primary 

at break. 
What is the effect of this induced E. M. F.? 
What happens as this E. M. F. dies out and what effect is 

produced upon the flux through the core? 
What effect has this upon the secondary? 
What indicates this? 




Induction Coil 
Fig. 16. 

CHAPTER 34. 

329. a. A cell whose E. M. F. is 1.4 volts is furnishing a current of 5 

amperes. To measure this current the circuit is broken and 
an ammeter is inserted. The resistance of the ammeter is 
.05 ohm. What current will it read when the circuit is closed? 
b. By what per cent is the original current changed? 

330. Arrange the following groupings of 12 cells and in each case in- 

dicate an ammeter connected to read the current and a 
voltmeter to read the E. M. F. of the battery: 

a. All in series. 

b. All in parallel. 

c. 4 in series, 3 in parallel. 



52 

331. a. A voltmeter whose resistance is 2000 ohms is shunted between 

two points, A and B, of a circuit between which the resistance 
is 1 ohm. With a current of 5 amperes flowing in the circuit 
in each case, compare the difference of potential between A 
and B before the voltmeter was connected up to that after 
it was connected. 
b. Is the voltage between A and B materially changed by the 
shunting in of the voltmeter? 

332. The difference of potential between two mains is greater than can 

be measured direct by the voltmeters on hand, the maximum 
scale reading of these instruments being only 150 volts. 
Two connected in series between the mains give readings of 
110 and 100 volts respectively. The resistance of the first 
is 17,000 ohms. Find the resistance of the second. 

333. The difference of potential between the two leads of an electric 

lighting circuit is 210 volts. The maximum scale reading of 
voltmeters on hand is 150 volts. Two of these instruments, 
A and B, are connected in series between the leads. The 
resistance of A is 15,000 ohms, that of B is 20,000 ohms. 
What are the readings of A and Bl 

334. a. What is the function of an ammeter? 

b. How is it usually connected? 

c. Is its resistance large or small? Why? 

d. What is the function of a voltmeter? 

e. How is it usually connected? 

/. Is its resistance large or small? Why? 

335. a. Five dry cells, each of an E. M. F. of 1.4 volts and an internal 

resistance of 0.3 ohm, are arranged in series. What is the 
reading of a voltmeter connected across the terminals of the 
battery? 
b. A current of 4.5 amperes is drawn from the battery. What is 
now the reading of the voltmeter? 

336. a. An unknown resistance and an ammeter are connected in series 

with a battery. The ammeter reads 2 amperes while a 
voltmeter shunted across the battery terminals reads 9.8 
volts. When the circuit through the ammeter is broken, the 
voltmeter reads 10 volts. Find the resistance of the battery. 
b. Find the resistance of the external circuit. 



53 

337. a. A battery has an E. M. F. of 100 volts and an internal resist- 

ance of 10 ohms. A voltmeter whose resistance is 1,000 ohms 
is connected across the terminals. What voltage does it read? 

b. A second voltmeter whose resistance is 10,000 ohms is substi- 

tuted for the first. What voltage does it read? 

c. What conclusion do you draw as to the resistance of a voltmeter 

and why? 

338. a. A battery is sending a current of 2 amperes through a cir- 

cuit. A voltmeter across the terminals of the battery reads 
17 volts. When the resistance of the circuit is decreased 
until the current is 3 amperes, the voltmeter reads 15.5 volts. 
Find the E. M. F. of the battery. 
b. Find the resistance of the battery. 

339. a. A voltmeter whose resistance is 20,000 'ohms is connected in 

series with a battery whose internal resistance is 3 ohms. If 
the voltmeter could be read exactly, by what fraction 
(decimal) would it fall short of the true voltage of the battery? 
b. By what instrument may the voltage of a battery be determined 
exactly? 

340. a. Make a diagram showing a battery delivering current to an 

external circuit and a voltmeter connected across the termi- 
nals of the battery. 

b. The E. M. F. of the battery is 200 volts and its resistance is 

2 ohms. The voltmeter reads 160 volts. Find the lost volts. 

c. Find the current in the circuit. 

d. Find the external resistance. 

341. The resistance of a switchboard shunt is .00125 ohm. An ammeter 

whose resistance is .05 ohm is connected in parallel with this 
shunt. Its scale readings multiplied by 100 indicate the cur- 
rent in the circuit. Find the resistance of the leads by which 
the ammeter is connected to the shunt. 

342. A conductor of No. 10 wire, resistance .001 ohm per foot, is carry- 

ing a current. We desire to measure this current without 
cutting the wire. An ammeter whose resistance is .005 ohm 
is connected by leads of a resistance of .001 ohm to points on 
the wire 3 feet apart and reads 6 amperes. Find the current 
in the main circuit. 



54 

343. The scale of a voltmeter whose resistance is 1700 ohms is gradu- 

ated to read to the nearest volt. Find the resistance to be 
connected in series with this instrument so that the scale 
divisions may indicate 5 volts. 

344. Upon testing a voltmeter whose resistance is 18,000 ohms, its 

readings are found to be 5 per cent too great. What resist- 
ance connected in series with the instrument will cause the 
readings to be correct? 

345. A voltmeter whose resistance is 1700 ohms is connected in series 

with a resistance of 10,000 ohms between two leads and reads 
16 volts. Find the difference of potential between the leads. 

346. An ammeter whose resistance is .05 ohm is graduated to read to 

the nearest ampere. Find the resistance which connected 
in series with this instrument will cause its scale to indicate 
volts. 

347. a. A millivoltmeter whose resistance is 10 ohms has 300 scale 

divisions. What current will drive the needle entirely across 

the scale? 
6. How can it be arranged for use as a voltmeter, each division of 

the scale to read 0.5 volt? 
c. How can it be arranged for use as an ammeter, each division of 

the scale to read .05 ampere? 

CHAPTER 35. 

348. a. While a current is flowing through a bare wire, a portion of the 

wire is dipped into a vessel of mercury. What change, if any, 
takes place in the current? 
6. What change, if any, takes place in the temperature of the part 
of the wire which is not dipped into the mercury? 

349. a. A constant E. M. F. is applied to the ends of a wire two meters 

long. One meter of the wire is then removed and in its place 
is inserted one meter of wire of the same material but of twice 
the diameter. What change takes place in the current? 
b. Compare the heating effects upon the meter of smaller wire. 

350. The ordinary 16 candle-power incandescent lamp requires a cur- 

rent of one-half ampere at a pressure of 110 volts. Find the 
heat developed in the lamp in 5 minutes. 



55 

351. a. Make a diagram of a voltmeter connected to read the difference 

of potential between the terminals of an incandescent lamp 
and an ammeter connected to read the current. 
b. The voltmeter reads 110 volts, the ammeter 0.5 ampere. Find 
the heat developed per second. 

352. a. A current of 3 amperes flows for 15 seconds through a coil 

whose resistance is 5 ohms and which is immersed in 10 grams 
of water. Find the number of calories imparted to the water. 
6. Find the resulting temperature of the water if the temperature 
at the beginning was 20° C. 

353. A coil whose resistance is 0.4167 ohm is placed in 1000 grams of 

water in Joules' apparatus and a current of 5 amperes is 
sent through it for 10 minutes. If the initial temperature 
of the water was 16° C, what was its final temperature? 

354. A wire whose resistance is 4 ohms is immersed in a bucket con- 

taining 15 liters of water. A current of 40 amperes is sent 
through the wire for 3 minutes. Find the rise in the tempera- 
ture of the water. 

355. A current of 5 amperes is passed through a coil of 10 ohms resist- 

ance immersed in 500 grams (about a pint) of water. The 
initial temperature of the water is 16° C. Find how long 
the current must flow in order to bring the water to the 
boiling point. 

356. 12 cells each of an E. M. F. of 1.5 volts and an internal resistance 

of 0.25 ohm, are connected in series with a certain resistance 
coil. The difference of potential across the battery terminals 
is 15 volts. When a second coil is substituted for the first, 
this difference of potential falls to 12 volts. Compare the 
quantity of heat developed in each coil in equal intervals. 

357. A current of 30 amperes is passed for 5 minutes through a coil of 

wire immersed in a liter of water. During this time, the 
difference of potential between the ends of the coil is 5.19 
volts and the temperature of the water increases 11.125° C. 
From this experiment deduce the relation between the joule 
and the calorie. 

358. A calorie is equivalent to approximately 3.1 foot-pounds. How 

many foot-pounds per minute are required by an arc light 
which takes 12 amperes at 50 volts? 



56 

CHAPTER 36. 

359. a. The internal resistance of a battery is the same as that of 2 

yards of a given wire. The external circuit is one yard of 
this wire. Compare the heat developed inside the battery in 
5 minutes to that developed on the outside in the same time. 

b. Make the external circuit 5 yards of the wire and again compare 

the heat developed inside and outside in the same time. 

c. Find the ratio of the power lost in the first case to that lost in the 

second. 

360. a. Make a diagram of an arc light with a voltmeter connected to 

read the difference of potential between the terminals and an 
ammeter to read the current. 

b. The voltmeter reads 50 volts, the ammeter 10 amperes. Find 

the resistance of the lamp. 

c. Find the heat developed per second. 

d. Find the power required to run the lamp. 

361. a. 12 incandescent lamps, each requiring 1 ampere at 100 volts, 

are arranged 2 in series, 6 in parallel. They are supplied by 
a battery whose E. M. F. is 240 volts and resistance 4 ohms. 
The resistance of the lead wires is 1 ohm per mile. At what 
distance from the battery can the combination be run? 

6. Find the power lost in the leads. 

c. Find the power lost in the lamps. 

362. a. A power plant is delivering current to a trolley line at a pres- 

sure of 550 volts. The resistance of the trolley wire is 0.32 
ohm per mile. A car 2 miles from the power plant is receiv- 
ing 75 amperes. Find the power delivered to the car. 

b. Find the horse-power delivered. 

c. What per cent is this of the total power delivered to the line? 

363. A lamp supplied with 1/2 ampere at 110 volts produces 16 candle- 

power. Find the candle-power that would be produced by 
these lamps per horse-power. 

364. a. A current of 1/2 ampere flowing through a lamp generates 

150 calories in 10 seconds. Find the resistance of the lamp. 
b. Find the power expended in lighting the lamp. 

365. a. Find the power required to run 150 lamps, each requiring 1/2 

ampere at 110 volts. 
b. These lamps are in parallel between leads whose resistance is 
2 ohms. Find the power lost in the leads. 



57 

366. Find the number of 55-watt lamps, each of a resistance of 220 ohms, 

which can be run in series by a generator which maintains 
a constant voltage of 2250, the resistance of the leads being 
100 ohms. 

367. Our power plant generates direct current at 240 volts. If the re- 

sistance of the leads from the power house to the laboratory 
be 0.25 ohm, what power is supplied to the laboratory when 
a current of 40 amperes is used? 

368. a. Make a diagram of an ammeter and a voltmeter connected so 

as to measure the power given to an arc lamp. 

b. The voltmeter reads 40 volts, the ammeter 10 amperes. Find 

the heat developed per second. 

c. Find the power given to the lamp. 

369. a. Make a diagram of a wattmeter connected to measure the 

power given to an incandescent lamp. 
b. A current of 1/2 ampere is flowing through a resistance of 220 
ohms. Find the heat developed in one hour. 

370. a. A 100-kilowatt generator at a waterfall is supplying power to 

a factory ten miles away over a wire whose resistance is 0.5 
ohm per mile. One per cent of the power is lost in the line. 
Find the current and voltage. 
b. Find the line loss if the current were doubled, the power re- 
maining the same. 

371. a. Six incandescent lamps, each requiring 1 ampere at 100 volts, 

are arranged, first, all in parallel; second, 3 in series, 2 in 
parallel. Find the current to run each combination. 

b. The length of the leads from the dynamo to each combination 

is the same. Find the cross-section of these leads so that in 
each set there is the same loss of power. 

c. Which arrangement is the more economical to install, and how 

much so? 

372. In transmitting power by a 100-volt circuit, the line loss is 40 per 

cent. The voltage is increased to 1000. What is now the 
line loss? 

373. In transmitting power to a distance by means of a 250-volt current. 

the estimated cost of the copper wiring was $1000. If the 
voltage be increased to 2500 and the same line loss be allowed, 
what saving can be made in the cost of copper? 



58 

374. a. A cubic inch of copper weighs 0.321 pound. To transmit 100 

amperes without heating the insulation beyond the limits 
allowed by the insurance companies requires a copper wire 
of 0.29 inch diameter. What size wire would be required 
if 100 amperes at 110 volts were transformed to 5 amperes at 
2200 volts? 
6. If copper wire costs 23 cents per pound, compare cost of wiring 
to transmit power to a distance of 10 miles. 

CHAPTER 37. 

375. a. The ordinary 110- volt, 16 candle-power, incandescent lamp 

requires one-half ampere. Find the power. 

b. Find the watts per candle-power. 

c. Find the candle-power per watt. 

d. How many of these lamps may be run by one horse-power? 

e. How many by a kilowatt? 

376. a. At 5 cents per kilowatt-hour, what is the cost of the light from 

an ordinary 16 candle-power, 55-watt lamp which in the course 
of a year runs for 1000 hours? 
b. What saving would result by substituting a tungsten 24- watt 
lamp? 

377. A difference of potential of 112 volts is maintained between the 

leads supplying the houses along a street. A house is fur- 
nished with 150 lamps in parallel, each requiring 1/2 ampere. 
Find the resistance of the leads from the street to the house 
so that when all the lamps are turned on, the voltage sup- 
plied to the lamps will not fall below 110. 

378. A given incandescent lamp requires 1 ampere at 100 volts. How 

many of these lamps, 2 in series, x in parallel, can be run by 
battery whose E. M. F. is 240 volts and internal resistance 
2 ohms? Neglect resistance of the leads. 

379. a. Make a diagram of 6 incandescent lamps arranged in parallel 

and a voltmeter connected to read the difference of potential 
between the leads. 

b. Each lamp requires a current of 1 ampere and an E. M. F. of 

100 volts. Find the resistance of the lamps. 

c. Find the current in the leads. 

d. Find the voltage indicated by the voltmeter. 



59 

a. Eight incandescent lamps, each of a resistance of 100 ohms and 

requiring an E. M. F. of 100 volts, are arranged (1) all in 
series, (2) all in parallel, (3) 4 in series, 2 in parallel. Find 
the resistance of each combination. 

b. Find the E. M. F. for each combination. 

c. Find the current for each combination. 

d. Find the power for each combination. 

a. A certain battery will deliver 10 amperes to an external cir- 

cuit provided the resistance of the circuit does not exceed 60 
ohms. Find the maximum number of incandescent lamps, 
each requiring 1 ampere and having a resistance of 100 ohms, 
that can be run by the battery. 

b. Make a diagram of the arrangement. 

a. A certain number of incandescent lamps, each requiring 1 ampere 

at 100 volts, are to be run by a battery whose E. M. F. is 175 
volts and resistance 0.7 ohm. The resistance of the leads is 
0.8 ohm. Find the number that can be run in parallel. 

b. Find the number that can be run in series. 

c. Find the horse-power developed by the battery, lamps in parallel. 

d. Of the total power developed by the battery, what per cent is 

used in the lamps? 

a. Make a diagram of a battery running 10 incandescent lamps in 

series. Indicate a voltmeter connected to read the difference 
of potential between the extremities of the group of lamps. 

b. Each lamp requires 1 ampere at 100 volts. Find the resistance 

of the group. 

c. Find the current in the circuit. 

d. Find the reading of the voltmeter. 

a. Make a diagram of a battery running 6 incandescent lamps 

arranged (1) all in series, (2) all in parallel, (3) 2 in series, 3 
in parallel. 

b. Each lamp requires 100 volts and has a resistance of 200 ohms. 

Find the voltage to run each combination. 

c. Find the current for each combination. 

d. Find the power for each combination. 

e. Find the heat developed in 5 minutes by each combination. 

a. Make a diagram of a battery sending a current through 6 
incandescent lamps arranged (1) all in series, (2) all in par- 
allel, (3) 3 in series, 2 in parallel. (Over.) 



60 

385. b. Each lamp has 100 ohms resistance and requires 1 ampere. 

Find the resistance for each combination. 

c. Find the current for each combination. 

d. The resistance of the battery is 1 ohm. Find what its E. M. F. 

must be for each combination. 

386. a. Make a diagram of a battery running 24 incandescent lamps 

in series. 

b. Each lamp requires 1 ampere and has a resistance of 100 ohms. 

The resistance of the battery is 2 ohms and the resistance of 
the leads is negligible. Find the total resistance of the circuit. 

c. Find the E. M. F. required of the battery. 

d. Find the lost volts. 

387. a. A battery has an E. M. F. of 650 volts and a resistance of 1 

ohm. A given incandescent lamp requires 100 volts and has 
a resistance of 200 ohms. Find the number of these lamps, 
6 in series, x in parallel, that can be run by the battery. 

6. Find the power used in the lamps. 

c. Find the energy lost in the battery in 1 hour. 

388. a. Make a diagram showing 10 arc lamps in series. 

b. The current is 10 amperes. Each lamp requires 50 volts and 

produces a back E. M. F. of 40 volts. The resistance of the 
leads is 5 ohms. Find the E. M. F. required in the circuit. 

c. Find the resistance of a lamp. 

389. a. Make a diagram of a battery running a number of arc lights 

in series. 
b. The resistance of the battery is 5 ohms. Each light requires 
10 amperes at an E. M. F. of 50 volts. 90 per cent of the 
power is used in the lights. Find the total number of lights. 

390. a. A battery has an E. M. F. of 320 volts and a resistance of 2 

ohms. A given arc lamp whose resistance is 1 ohm requires 
10 amperes and gives a back E. M. F. of 30 volts. Find the 
number of lamps in series that the battery will run. 

b. Find the lost volts. 

c. Find the heat developed in the battery in 1 hour. 

391. a. Make a diagram of 6 arc lamps in series. Each takes a current 

of 10 amperes at 50 volts and gives a back E. M. F. of 40 
volts. Find the resistance between the terminals of the series. 

b. Find the difference of potential between these terminals. 

c. Find the heat developed in the lamps in 5 minutes. 



61 

392. a. Make a diagram of a battery running 10 arc lamps in series. 

b. The battery has an E. M. F. of 540 volts and a resistance of 3 

ohms. The resistance of the lead wires is 6 ohms. Each lamp 
requires 45 volts and has a resistance of 1 ohm and a back 
E. M. F. of 35 volts. Find the power used by the lamps. 

c. Find the power lost by the battery. 

d. What per cent of the power is lost in the battery and leads? 

CHAPTER 40. 

393. The maximum number of lines of force embraced by a coil of a 

bipolar alternator is 10,000. The coil makes 30 revolutions 
per second. Find the maximum induced E. M. F. in the coil. 

394. At a locality where the horizontal component of the earth's mag- 

netism is 0.19, a circular coil of wire of 25 centimeters radius 
and 50 turns rotates about a vertical axis 15 times per second. 
Find the maximum E. M. F. induced in the coil. 

395. a. AB represents the cross-section of a coil rotating about the 

axis C in a uniform magnetic 

field NS. Assume the direc- 

5 tion of rotation and plot the 

curve of induced E. M. F. for 

one complete revolution. 



N 



B© 



Fi s- 17 - b. Mark on the diagram the points 

of maximum and of zero induction and indicate the corre- 
sponding ordinates of the E. M. F. curve. 
c. The resistance of the coil is 2 ohms; plot the current curve. 

396. a. Construct a curve to represent an alternating current. 

b. Construct a curve to represent a rectified current. 

c. By what device may an alternating current in a generator be 

converted into a direct current in the external circuit? 

397. a. AB represents the cross-section of a coil of 3 turns rotating in 

eg A a clockwise direction in the uni- 

form magnetic field NS. In 
what position of the coil is the 
induced E. M. F. a maximum? 
b. On rectangular axes construct the 
E. M. F. curve for one turn of 

the coil. 

<& B c. On the same axes construct the 

Fig - 18 ' E. M. F. curve for the entire coil. 

d. What is the effect of increasing the number of turns of the coil? 



62 

398. a. A, B and C represent the end view of 3 rectangular coils rotat- 
ing in a clockwise direction in a uniform magnetic field NS. 
Indicate on each end of each coil the direction of the induced 
E. M. F. 







Fig. 19. 

b. Indicate direction of current in external circuit. 

c. On rectangular axes construct the E. M. F. curves for the three 

coils, lettering them to correspond to the respective coils. 
On the same axes construct the curve of the resultant E. M. F. 

in the external circuit. 
Indicate change that this curve would undergo if number of 

coils be doubled. 



d. 



e. 



399. a. The coils A and B are rotating in a clockwise direction in the 
uniform magnetic field NS. Apply right-hand rule and deter- 
mine direction of E. M. F. in each side of each coil. 




h. 



c. 



On rectangular axes construct the E. M. F. curves for each coil, 
lettering each to agree with corresponding coil. 

Are the E. M. F.s in the separate coils in conjunction or in op- 
position? Why? 

Construct curve of resultant E. M. F. and indicate direction 
of E. M. F. acting in external circuit. 



63 

400. a. A shunt-wound generator is supplying to the external circuit 

a current of 200 amperes. The voltage across the brushes is 
110. The current through the shunt field-coil is 6 amperes. 
The resistance of the armature is .03 ohm. Find the current 
through the armature. 

b. Find the total E. M. F. 

c. Find the resistance of the shunt coil. 

d. Find the external resistance. 

401. a. Make a diagram of a shunt- wound generator supplying current 

to a group of 100 incandescent lamps in parallel, each re- 
ceiving 1/2 ampere at 110 volts. The resistance of the 
armature is .04 ohm, that of the shunt field coils is 45 ohms 
and that of the leads is .05 ohm. 

b. Find the potential across the brushes. 

c. Find the E. M. F. of the generator. 

d. Find the watts lost in the armature. 

e. Find the watts lost in the shunt field. 
/. Find the watts lost in the leads. 

g. Find the watts used in the lamps. 

h. Find the electrical efficiency of the generator, i. e., the ratio 
of the useful watts to the total watts developed. 

402. a. Make a diagram of a compound short-shunt generator sup- 

plying current to a group of lamps in parallel. 

b. Make a diagram of a compound long-shunt generator similarly 

connected. 

c. In each case the E. M. F. of the generator is 120 volts, the 

armature resistance is .04 ohm, the resistance of the series 
field -coils is .02 ohm, that of the shunt field-coils is 45 
ohms and the resistance of the leads and lamps is 21 ohms. 
Compare the currents through the shunt field-coils in each 
case. 

403. A generator whose field is of constant strength and whose internal 

resistance is 0.2 ohm is driven by a belt applied to an 8-inch 
pulley and develops an E. M. F. of 200 volts. It is desired 
to charge a storage battery whose E. M. F. is 145 volts 
and resistance 0.8 ohm with a current of 15 amperes from 
this generator. Find the diameter of the pulley which if 
substituted for the original pulley will enable this to bo 
done. 



64 



404. a. Make simplest form of diagram of a series-wound generator 

supplying current to an external circuit. Represent a rheo- 
stat shunted across the field coils. 
b. The machine runs at constant speed and delivers a constant cur- 
rent. The E. M. F. varies directly with the current through 
the field coils whose resistance is 0.2 ohm. With no current 
through the rheostat, this E.M.F. is 120. Find the resistance 
to be used in the rheostat to reduce this voltage to 110. 

405. a. A continuous coil is wrapped around the rim of an iron-tired 

wagon wheel, the turns being put on in a clockwise direction 
looking along the tire. The wheel is then put on a horizontal 
east and west axle and is spun so that the north side moves 
downward. Indicate the direction of the E. M. F. induced 
in the turns. 

Give rule for determining this direction. 

Indicate points of maximum and minimum E. M. F. 

Indicate the current in the external circuit. 
b. Construct the E. M. F. curve due to the coil in vertical plane. 

C 



b. 

c. 

406. a. 




407. 



D 
Fig. 21. 

c. On the same axes construct the simultaneous values of the 

E. M. F. curve due to the coil in the horizontal plane. 

d. Construct the resultant curve. 

e. How may the resultant E. M. F. be made practically constant? 

The resistance of the wire used in the armature coils of a series- 
wound bipolar generator is 4 ohms. The machine has an 
E. M. F. of 125 volts. What is the reading of a voltmeter 
connected across the brushes when the machine is delivering 
16 amperes? 



65 

408. a. Complete the diagram herewith (Fig. 22) as a series-wound 
generator. Letter the poles, indicate the direction of rota- 
tion of the armature, the direction of the E. M. F. in the in- 
ductors and the direction of the current in the field coils. 
Locate the brushes and represent an external circuit supply- 
ing a group of 6 incandescent lamps in parallel. Indicate the 
direction of the current in the external circuit. 
6. Each lamp takes 100 volts and has 100 ohms resistance. The 
resistance of the leads is 20 ohms. Find the E- M. F. across 
the brushes. 




Fig. 22. 



(Over.) 



66 

408. c. The armature resistance is 0.5 ohm. Find the E. M. F. of the 

generator. 
d. Find the maximum current carried by an inductor. 

409. a. Complete the diagram of problem 408 as a shunt-wound 

generator. Letter the poles, indicate the direction of rota- 
tion of the armature, the direction of the E. M. F. in the 
inductors and the direction of the current in the field coils. 
Locate the brushes and represent an external circuit supply- 
ing a group of 10 incandescent lamps in parallel. Indicate 
the direction of the current in the external circuit. 

b. Each lamp receives 1 ampere at 100 volts. Find the resist- 

ance of the group of lamps and the current in the main 
circuit. 

c. The resistance of the leads is 2 ohms and the resistance of the 

field coils is 40 ohms. Find the current through the field 
coils. 

d. The armature resistance is 1.5 ohms. Find the E. M. F. of the 

generator. 

e. Find the maximum current carried by an inductor. 

410. a. Complete the diagram of problem 408 by placing a series 

coil about the yoke of the field magnets and wiring the ma- 
chine as a compound short-shunt generator. Letter the poles, 
indicate the direction of rotation of the armature, the direc- 
tion of the E. M. F. in the inductors and the direction of the 
current in the field coils. Locate the brushes and represent 
an external circuit supplying a group of 8 incandescent lamps 
in parallel. Indicate the direction of the current in the ex- 
ternal circuit. 

b. Each lamp receives 1/2 ampere at 110 volts. Find the resistance 

of the group and the current in the main circuit. 

c. The resistance of the leads is 2 ohms, that of the shunt field 

coils is 39-1/3 ohms, and that of the armature is 1 ohm. 
Find the E. M. F. of the generator. 

411. a. Make a diagram of an 8-coil ring armature for a bipolar genera- 

tor with two turns per coil. 
6. Indicate direction of field, direction of rotation and direction 

of induced E. M. F. in coils, 
c. Locate brushes and indicate direction of current in external 

circuit. 






67 



412. The resistance of the wire used in the armature coils of a four-pole 

generator is 4 ohms. The machine has an E. M. F. of 75 
volts. What current will it deliver when used to charge a 
storage battery whose E. M. F. is 60 volts and whose re- 
sistance is 1 ohm? 

413. a. Make a star development of the winding represented in the 

following diagram. 
b. Is it a wave winding or a lap winding? 




Fig. 23. 

414. a. Make a star development of the winding represented in the 
following diagram. 
b. Is it a wave winding or a lap winding? 




Fig. 24. 

415. There is a flux of 3,000,000 lines between the poles of a bipolar 

generator. There are 200 inductors on the armature. Find 
the rate at which the armature must rotate in order to gen- 
erate 120 volts. 

416. In winding the armature of an 8-pole lap-wound generator, there 

was used a coil of wire whose resistance was 2 ohms. The 
machine has 480 inductors and makes 600 revolutions per 
minute. The flux from each pole is 4,000,000 lines. Find 
the voltage across the brushes when the machine is delivering 
16 amperes. 



68 

417. a. A 6-pole lap-wound generator with 240 inductors on the arma- 

ture makes 600 revolutions per minute. The flux from each 
pole is 6,000,000 lines. Find the E. M. F. 
b. Had this generator been wave-wound, what would the E. M. F. 
be? 

418. a. Make a diagram of the 3 wire system for incandescent lamps 

with 2 lamps on the upper and 4 on the lower side of the 
neutral wire. 

b. Make a similar diagram with 5 lamps on the upper and 4 on the 

lower side. Indicate the direction of the currents in the leads 
in both cases. 

c. Each lamp requires 1/2 ampere at 110 volts. The resistance of 

each lead is 1 ohm. What is the difference of potential across 
the brushes of the generators in each case? 

419. a. Make a diagram of the 3 wire system for incandescent lamps 

with 6 lamps on the upper and 5 on the lower side of the 
neutral wire. Indicate the direction of the current in the 
three leads. 
b. Each lamp requires an E. M. F. of 110 volts and a current 
of 1/2 ampere. The resistance of each generator and of 
each lead is 1 ohm. When the lamps are receiving proper 
current, what E. M. F. is being produced by each gen- 
erator? 

420. In the 3 wire system represented in the figure, each generator 

maintains a constant voltage of 110 across its brushes. 



2 OH^ 



|J10 v 



QQ66Q 



• 2 OHM 



9*9 



-3 OHM 



JiO V 



66666666?0"5 



.5 OHM 



Fig. 25. 

Each lamp takes 1 ampere. How many lamps should be 
turned on in x so that the voltage across this group shall be 
the same as the voltage across the group below? 



69 

421. a. Make a diagram of 4 generators supplying a 5 wire system. 

Place in the upper space a group of 3 lamps, in the next 4, in 
the next 2 and in the last 5. 

b. Each lamp requires 1 ampere at 100 volts. The resistance of 

each lead is 2 ohms and that of each generator is 1 ohm. Find 
the E. M. F. across the brushes of each generator when all the 
lamps are receiving the proper current. 

c. Find the E. M. F. of each generator at this time. 

CHAPTER 41. 

422. A generator whose E. M. F. is 100 volts and whose internal resist- 

ance is 0.2 ohm is supplying 15 amperes to an external circuit. 
The speed of the generator is increased until a voltmeter 
across the brushes reads 116.4 volts. What current is the 
generator now supplying? 

423. A shunt-wound generator is used to charge a storage battery of 55 

cells. The resistance of the battery and its leads is 1 ohm, 
The voltage of each cell when receiving charge is 2.4 volts. 
Find the voltage across the brushes of the generator when 
the charging current is 10 amperes. 

424. A generator has an internal resistance of 20 ohms and is sending a 

current of 10 amperes through the external circuit. The 
difference of potential between the brushes is 500 volts. A 
given cell has an E. M. F. of 1 volt and an internal resistance 
of 2 ohms. Find the number of cells, x in series, y in parallel, 
required to replace the generator so that there would be the 
same loss of power in the cells that there is in the generator. 

425. a. Make simplest form of diagram of a series- wound and of a 

shunt-wound generator. Suppose each to be connected to an 
external circuit and to be run at constant speed. 

b. In the series generator, suppose the resistance in the external cir- 

cuit to be decreased. What change in the current will result? 

c. What change will this produce in the strength of the field mag- 

nets? 

d. What change in the voltage will follow? 

e. In the shunt machine, suppose the resistance in the external cir- 

cuit to be decreased. What change in the current will result? 
/. How does this affect the drop of potential across the armature? 
g. What change in the difference of potential between the brushes 

results? (Over.) 



70 

425. h. How does this affect the current in the field coils? 

i. What change will this produce in the strength of the field 

magnets? 
j. What change in voltage will follow? 

426. a. A generator whose internal resistance is 0.1 ohm is furnishing 

100 amperes to an illuminated sign on which 110-volt lamps 
are grouped in parallel. The resistance of the leads is 0.9 
ohm. If 40 horse-power is spent in driving the generator, 
what is the commercial efficiency of the plant, i. e., the ratio 
(percentage) of the useful power developed to the total power 
supplied to the generator? 
b. What is the electrical efficiency of the transmission, i. e., the 
ratio (percentage) of the power delivered to the lamps to the 
useful power developed? 

427. a. Make simplest diagram of a series-wound generator. 

b. The resistance of the field coils and armature is 0.5 ohm. When 

a current of 4 amperes is being delivered, the difference of 
potential across the terminals is 30 volts. Find the E. M. F. 
of the generator. 

c. Assuming the speed of the generator to be constant and that 

the magnetization of the field magnets varies as the square 
root of the current, find the difference of potential across the 
terminals when the current is successively made 49, 100, 200 
and 400 amperes. 

d. Draw to scale the external characteristic of this generator. 

428. a. Make simplest diagram of a shunt-wound generator. 

b. The armature resistance is 0.1 ohm, the shunt field resistance 

25 ohms and when a current of 5 amperes is flowing in the 
external circuit, the E. M. F. across the brushes is 100 volts. 
Find the E. M. F. of the generator and the current in the 
field coils. 

c. The current in the external circuit is changed to I amperes. 

Calling the E. M. F. across the brushes E, find an expression 
for the current through the field coils, thence for the total 
current, thence for the drop across the armature and thence 
for the E. M. F. of the generator. 
d. Assuming that the magnetization of the field magnets varies as the 
square root of the current through the field coils and that the 
speed of the generator is constant, find the E. M. F. across the 
brushes when the current in the external circuit is 25 amperes. 



71 

429. a. How is a generator over-compounded? 

b. A 240-volt generator running the lights in a factory is over- 
compounded so as to furnish constant potential to the lamps. 
If the resistance of the leads be 0.1 ohm, what is the E. M. F. 
across the brushes when the generator is delivering 250 
amperes? 

430. a. An over-compounded generator, whose internal resistance is 

.05 ohm, supplies current for the 110-volt lamps in a distant 
factory building. The resistance of the leads is 1 ohm. When 
the machine is delivering 50 amperes, what E. M. F. does it 
develop? 
6. What is the E. M. F. across the brushes? 

CHAPTER 42. 

431. On the armature of a motor there are 200 inductors each 40 centi- 

meters (about 16 inches) long. They lie in a uniform mag- 
netic field of 6,000 lines per square centimeter. Find the 
force in pounds acting upon the armature when a current of 
30 amperes is sent through the inductors. 1 pound = 445,000 
dynes. 

432. A motor connected across 110-volt leads develops a back E. M. F. 

of 104 volts and takes an armature current of 20 amperes. 
Find what this current would become if the motor were sud- 
denly stopped. 

433. a. A motor whose resistance is 0.2 ohm and whose field is constant is 

running a certain machine and taking an armature current of 
12 amperes from 110-volt leads. Find the back E. M. F. 
b. The load is varied and the armature current drops to 6 amperes. 
What change takes place in the speed of the motor? 

434. a. A generator whose E. M. F. is 250 volts and internal resistance 

0.5 ohm is charging a storage battery whose E. M. F. is 220 
volts and internal resistance 1 ohm. The resistance of the 
leads is 0.5 ohm. The battery is shunted with a motor which 
is taking 40 amperes. Make a diagram of the arrangement. 

b. Does the generator supply this entire current? Why? 

c. Of the total power delivered to the motor, what per cent, if any, 

is furnished by the battery? 

d. What current is delivered by the generator when no current 

flows through the battery? 



72 

435. A storage battery has an E. M. F. of 112 volts and an internal 

resistance of 2 ohms. It is being charged with a current of 
15 amperes. Find the difference of potential between its 
terminals. 

436. A motor whose internal resistance is 0.25 ohm is receiving a 

current of 30 amperes. A voltmeter across its brushes 
reads 100 volts. What is the back E. M. F. of the 
motor? 

437. A motor whose resistance is 2 ohms is supplied with a current of 

10 amperes and develops 2 horse-power. Find the difference 
of potential across the brushes of the motor. 

438. A generator run at a certain speed develops an E. M. F. of 100 

volts. Its internal resistance is 0.35 ohm. When run as a 
motor at the same speed, a voltmeter across the brushes 
reads 104.2 volts. What current is it receiving? 

439. a. A generator is supplying current to a motor. The resistance 

between the brushes of the motor is 0.25 ohm; the resistance 
of the leads is 2 ohms. When a current of 5 amperes is flowing 
in the leads, a voltmeter across the brushes of the generator 
reads 110 volts. Find the back E. M. F. of the motor. 
b. What is the voltage across the motor brushes? 

440. a. Make a diagram of a generator running a motor and indi- 

cate a voltmeter connected across the brushes of the 
motor. 

b. Each machine has a resistance of 1 ohm and the resistance of 

the leads is 2 ohms. The E. M. F. of the generator is 200 
volts and the back E. M. F. of the motor when running at full 
speed is 100 volts. Find the reading of the voltmeter before 
the motor starts. 

c. Find the reading when the motor reaches full speed. 

441. a. A generator having an E. M. F. of 500 volts is running a motor 

which develops a back E. M. F. of 450 volts. Each machine 
has a resistance of 5 ohms. Find the power delivered to the 
motor. 

b. Find the power developed by the motor. 

c. Find the power lost due to the resistance. 

d. Find the difference of potential across the brushes of the 

motor. 



73 

42. a. A generator and a motor of equal resistance are connected in 

series. When the motor armature is held so that it can not 
rotate, the current through the circuit is 87.5 amperes and 
the E. M. F. across the brushes of the generator is 175 volts. 
The motor armature is now released and when it reaches full 
speed, the current is 25 amperes and the E. M. F. across the 
brushes of the generator is 300 volts. Find the total E. M. F. 
of the generator. 

b. What horse-power is developed by the motor? 

43. a. A motor whose resistance is 1 ohm is connected to mains 

between which a constant difference of potential of 110 volts 
is maintained. The resistance of the leads from the mains 
to the motor is 1 ohm. When the motor is running at full 
speed, the voltage across its terminals is 105. Find the 
current. 
6. Find the back E. M. F. 

c. Find the efficiency of the motor. 

44. a. Make simplest diagram of a shunt motor. 

b. The E. M. F. between the leads is 120 volts, the resistance of the 

shunt field is 60 ohms, that of the armature is 0.2 ohm, the 
total current 32 amperes. Find the current through the field 
coil and through the armature. 

c. Find the back E. M. F. 

[45. a. Make simplest form of diagram of a shunt motor. 

b. The E. M. F. between the leads is 240 volts, the armature 

resistance is 0.25 ohm and with no load the machine takes 2 
amperes. Find the back E. M. F. developed. 

c. Without changing any other condition, the armature speed is 

increased 3 per cent. What happens? 

[46. a. A shunt motor is connected between 120-volt leads and when 

running at full speed takes 12 amperes. The resistance of 

the field coils is 60 ohms, that of the armature is 0.5 ohm. 

Find the currents through the field and through the armature. 

b. Find the back E. M. F. developed by the motor. 

[47. A shunt motor whose armature resistance is 0.25 ohm is connected 
between 110-volt leads and makes 1,200 revolutions per 
minute. The armature current is 3 amperes. When a certain 
load is thrown upon the motor, the armature current rises to 
20 amperes. Find the speed at which it is now running. 



74 

448. a. Make a diagram of a shunt motor between 110-volt mains and 

place a rheostat between one of the mains and the armature. 
b. The resistance of the armature is 0.4 ohm. With no resistance 
in the rheostat and with an armature current of 3 amperes, 
the machine makes 1,200 revolutions per minute. Find the 
resistance that must be inserted in the rheostat so that with 
an armature current of 12 amperes the revolutions per minute 
will be only 900. 

449. a. A motor whose resistance is 0.5 ohm is connected across 120- 

volt leads. The coils can not safely carry a current in excess 
of 60 amperes. Find the resistance of the starting rheostat 
so that this current will not be exceeded. 
b. What is the voltage across the brushes just as the motor starts? 

450. a. A series motor whose resistance is 0.2 ohm is connected across 

120-volt leads and running under a certain load takes 50 
amperes. Find the back E. M. F. developed. 

b. A change takes place in the load and the motor now takes 20 

amperes. Find the back E. M. F. 

c. In the first case it made 600 revolutions per minute. Assuming 

the strength of the field magnets to vary directly with the 
current, find the speed in the second case. 



CHAPTER 43. 

451. a. The equation of an alternating current is I = lO.sin 6. 

The equation of a second current is I = 5.sin (0 + 30°). 

Construct the corresponding curves. 
6. Construct the curve of the resultant current, 
c. By means of a geometrical construction, find the maximum 

value of the resultant current. 

452. a. The rectangular coil AB, whose width is one-fourth of the 

distance between N and N, is moving to the right. The 

E. M. F. generated in each 
side of the coil is taken as 
varying with the sine of 
the angle through which 
the side has moved since 
Fi s- 26 - passing through the neu- 

tral plane. E. M. F. directed in at A and out at B is con- 
sidered positive. The field is a maximum below the center 
of each pole. Construct the curve of E. M. F. for the side A. 

(See next page.) 



N 


• 
B 


S 




N 




5 


• 
A 















75 

452. b. Construct the curve of E. M. F. for the side B. 

c. Compound these curves and find the position of the coil when 
the resultant E. M. F. is a maximum. 

453. The instantaneous value of an alternating current at the 45° phase 

is 250 amperes; find its value at the 60° phase. 

454. a. The instantaneous value of an alternating current at the 60° 

phase is 200 amperes; find its maximum value. 
b. Find its virtual value. 

455. a. The maximum value of an alternating E. M. F. is 500 volts; 

find its virtual value. 
b. Find its instantaneous value at the 60° phase. 

456. The virtual value of an alternating E. M. F. is 159 volts; find its 

instantaneous value at the 60° phase. 

457. The equation of an alternating current is 7 = 346.sin 0. 

At what phase will the current be 200 amperes? 

458. a. The equation of an alternating E. M. F. is 2£ = 354.sin 252f. 

Find the frequency. 

b. Find the maximum value. 

c. Find the virtual value. 

459. a. Draw to some convenient scale a curve representing an al- 

ternating current in a circuit having induction. Suppose 
this to represent also the E. M. F. in phase with the cur- 
rent. 

b. Draw the curve of self induction, the amplitude being one-half 

of that of the first curve. 

c. Draw a curve representing the E. M. F. required to overcome 

this self induction. 

d. Compound this last curve with the first. What does the 

resultant curve represent? 

e. Does it lead the current curve or lag behind it? 

460. a. Make a diagram showing an alternating current curve lagging 

30° behind its corresponding E. M. F. curve. Assume the 
maximum ordinate of the E. M. F. curve to be twice that of 
the current curve. 
b. Construct the maximum power component of the E. M. F. 



76 

461. a. Make a diagram of an alternating current curve leading an 

impressed E. M. F. curve. Make the maximum ordinate of 
the E. M. F. curve double that of the current curve. 

b. Decompose the current curve into two curves; one in phase 

with the impressed E. M. F., the other at right angles to it. 

c. Find the relation between the maximum ordinate of the current 

curve and the maximum value of its component in phase 
with the impressed E. M. F. 

462. a. The maximum current in an alternating circuit is 10 amperes. 

The resistance is 5 ohms. The maximum E. M. F. of self 
induction is 100 volts. Find the maximum impressed E. M. F. 

b. Make a diagram showing the current curve and the curve of 

self induction. 

c. Construct the curve of impressed E. M. F. 

d. Does the current lag or lead? 

463. Find the impedance of a circuit of 8 ohms resistance and 6 ohms 

inductive reactance. 

464. An E. M. F. whose frequency is 33 applied to a coil whose resist- 

ance is 10 ohms and inductance .02 henry produces a current 
of 18.48 amperes. Find the E. M. F. 

465. An E. M. F. whose frequency is 25 is applied to a coil whose resist- 

ance is 12 ohms and develops an impedance of 20 ohms. Find 
the inductance of the coil. 

466. An E. M. F. whose frequency is 25 is applied to a coil whose in- 

ductance is .05 henry and develops an impedance of 20 ohms. 
Find the resistance of the coil. 

467. a. An alternating E. M. F. of a frequency of 60 is applied to a 

circuit of 10 ohms resistance and .025 henry inductance. 
Find the impedance. 
b. Find the angle of lag. 

468. a. An alternating E. M. F. of 100 volts at a frequency of 100 is 

applied to a coil whose self induction is .025 henry and whose 
resistance is negligible. What current is produced? 
b. If a resistance of 10 ohms be connected in series with the coil, 
what current will flow? 

469. a. An alternating E. M. F. of 100 volts and a frequency of 120 

per second is applied to a coil whose resistance is 5 ohms and 
inductance .01 henry. Find the current. 
b. Find the angle of lag. 



77 

470. a. An alternating E. M. F. of 110 volts and frequency of 60 is 

applied to a coil whose resistance is 10 ohms and produces a 
current of 5 amperes. Find the inductance of the coil. 
b. Find the angle of lag. 

471. a. An alternating E. M. F. of a frequency of 100 is applied to a coil 

whose inductance is .005 henry and whose resistance is negli- 
gible. A current of 30 amperes is produced. Find the voltage. 

b. Find the angle of lag. 

c. Find the resistance that must be added to the circuit in order to 

make the angle of lag 45°. 

472. A bank of lamps requiring 10 amperes at 110 volts is to be con- 

nected to leads between which the voltage is 120 at a fre- 
quency of 100. Find the inductance that must be connected 
in series with the lamps so that they may receive the proper 
voltage. 

473. a. A circuit has a resistance of 4 ohms and an inductance of .04 

henry. An alternating E. M. F. of 100 volts and frequency of 
80 is applied. Find the maximum current. 
b. Find the angle of lag. 

474. a. An alternating E. M. F. of a frequency of 100 is applied to a 

coil whose resistance is 8 ohms and the resulting current lags 
45°. Find the inductance of the coil. 
b. If the E. M. F. was 100 volts, what current was produced? 

475. An alternating E. M. F. of 100 volts and a frequency of 100 is 

applied to a circuit of non-inductive resistance of 2 ohms. 
Find the inductance that must be added to the circuit in order 
that the current may not exceed 5 amperes. 

476. In an alternating current circuit, an incandescent lamp and an 

electromagnet of negligible resistance are connected in series. 
The drop across the lamp is 100 volts; that across the mag- 
net is 25 volts. Find the total drop across the two. 

477. In an alternating current circuit, a coil of negligible resistance but of 

considerable inductance is connected in parallel with an arc 
lamp. The current through the lamp is 8 amperes ; that through 
the coil is 6 amperes. Find the current in the main line. 

478. a. An alternating E. M. F. of 100 volts and a frequency of 60 is 

applied to a circuit of 10 ohms resistance and 20 microfarads 
capacity. Find the impedance. 
b. Find the current. 



78 

479. a. An alternating current of a frequency of 100 is applied to a 5 

microfarad condenser. Find the reactance. 

b. If the voltage be 100, find the current. 

c. Find the current when a resistance of 2 ohms is connected in 

series with the condenser. 

480. a. An alternating E. M. F. of 100 volts and a frequency of 60 is 

applied to a circuit of 10 ohms resistance, .025 henry induct- 
ance and 25 microfarads capacity. Find the impedance. 
b. Find the current. 

481. a. An alternating E. M. F. of 100 volts and a frequency of 60 is 

applied to a circuit of 10 ohms resistance, .025 henry induct- 
ance and 281 microfarads capacity. Find the impedance. 
b. Find the current. 

482. a. Find the impedance of a circuit of 14 ohms inductive reactance, 

5 ohms capacity reactance and 12 ohms resistance. 
b. Does the current lead or lag? Why? 

483. An alternating current circuit has an inductance of .05 henry and a 

capacity of 20 microfarads. Find the frequency at which the 
impedance is equal to the ohmic resistance. 

484. a. There are connected in series a coil L whose inductance is .03 

henry but whose resistance is negligible, a non-inductive 
resistance R of 5 ohms and a condenser K whose capacity is 
90 microfarads. An alternating E. M. F. of 125 volts at a 
frequency of 100 is applied to the extremities of the combina- 
tion. Find the impedance. 

b. Find the current. 

c. What is the difference of potential across the coil and across 

the condenser? 

485. A non-inductive resistance of 20 ohms, a resistanceless inductance 

of .06 henry and a condenser of 150 microfarads capacity are 
connected in series to 110-volt, 60-cycle leads. Find the drop 
across the resistance, the inductance and the condenser. 

486. Find the power factor of an alternating current circuit whose 

resistance is 100 ohms and inductance 0.2 henry, the fre- 
quency being 60. 

487. a. An alternating E. M. F. of 100 volts and a frequency of 60 is 

applied to a coil whose resistance is 6 ohms and inductance 
0.2 henry. Find the current. 

b. Find the angle of lag. 

c. Find the power developed in the coil. 



79 

CHAPTER 44. 

Fig. 27 represents diagrammatically an experimental alter- 
nator. The stationary armature is exterior and carries 12 
coils wrapped as shown. The ends of every pair of coils are 
carried to a board A and terminate there in the binding posts 




Fig. 27. 



80 

D, E, F, etc. For instance, coils 1 and 2 terminate in the 
posts / and H. To connect one pair of coils to the next, a 
wire must be inserted between the corresponding binding posts, 
as for example between K and I if coils 11-12 are to be con- 
nected to coils 1-2. A wavy line between two binding posts on 
A indicates that these posts are the terminals of a pair of coils. 
B and C are an extra pair of posts connected midway between 
the coils 9 and 10 and the coils 3 and 4, respectively. 

There are 10 poles in the revolving field and the rotation is 
clockwise. When the field turns through an angle of 72° 
(one-fifth of a circle), the E. M. F. in each coil passes through 
a complete cycle. 

488. a. Mark on each coil of the diagram herewith (Fig. 27) the direc- 

tion of the instantaneous E. M. F. and also mark this direc- 
tion alongside of the indicated coils on the board A. 

b. Connect all the coils on A in series. 

c. Attach a lead to G and one to N and represent a lamp between 

these leads. 

d. How does the voltage in these leads compare to that in one-half 

of the armature? 

e. How does the current in the leads compare to that in any coil? 

489. a. Mark on each coil of the diagram herewith (Fig. 27) the direc- 

tion of the instantaneous E. M. F. and also mark this direc- 
tion alongside of the indicated coils on the board A. 

b. Connect all the coils on A in series. 

c. Break connection between G and H and between N and and 

connect H to 0. Attach a lead to N and one to G and repre- 
sent a lamp between these leads. 

d. How does the voltage in these leads compare to that in one-half 

of the armature? 

e. How does the current in the leads compare to that in any coil? 

490. a. Mark on each coil of the diagram herewith (Fig. 27) the direc- 

tion of the instantaneous E. M. F. and also mark this 
direction alongside of the indicated coils on the board A. 

b. Connect all the coils on A in series. 

c. Attach a pair of leads to B and C and a pair to K and P and 

place a lamp between each pair. 

d. When will the current in BC be a maximum? 

e. At that moment what will be the current in KP1 
/. What is this arrangement of the alternator called? 



81 

491. a. Mark on each coil of the diagram herewith (Fig. 27) the direc- 

tion of the instantaneous E. M. F. and also mark this direc- 
tion alongside of the indicated coils on the board A. 

b. Connect all the coils on A in series. 

c. Attach leads to G, P and L and between these three leads 

arrange a delta grouping of lamps. 

d. Indicate direction of current through the lamps. 

e. How does the current in lead G compare to that in the coils 1-2? 

492. a. Mark on each coil of the diagram herewith (Fig. 27) the direc- 

tion of the instantaneous E. M. F. and also mark this direc- 
tion alongside of the indicated coils on the board A. 

b. Connect all the coils on A in series. 

c. Break connections between G and H, P and D, and L and M 

and connect D, H and M to a common point at A. Attach 
leads to G, P and L and between these three leads arrange a 
Y grouping of lamps. 

d. Indicate direction of current through the lamps. 

e. What is the object of this arrangement of the armature? 

493. The current from an A.C. generator is passed through a step-up trans- 

former, there being 600 turns in the primary and 4,200 in the 
secondary. At the distant end of the line it is passed through 
a step-down transformer having 17,500 turns in the primary 
and 500 in the secondary. The voltage required is 250. Neg- 
lecting all losses, what must be the E. M. F. of the generator? 

494. a. Make a diagram showing a step-up transformer and a step- 

down transformer connected to the same generator mains. 

b. The E. M. F. in the primary is 1,000 volts; the current is 1 am- 

pere; the number of turns is 100. The voltage is transformed 
to 5,000 by one transformer and to 100 by the other. Find 
the number of turns in each secondary. 

c. Find the current in each secondary. 

d. What is the current in the primary if both secondaries be open? 

495. a. Make a diagram showing a step-up and a step-down transformer 

connected to the same generator mains. 

b. The E. M. F. of the mains is 500 volts. Assume the number of 

turns in the primaries and find the number of turns in the 
secondaries so that one develops 2,500 volts, the other 100. 

c. The current in the mains is 2 amperes; find the current in each 

secondary. 

d. Find the power imparted to each transformer. 



82 



496. a. Make a diagram showing a transformer connected to the mains 

of a generator. 

b. Indicate a secondary circuit with 6 lamps in parallel. 

c. Draw a line of force due to the current in the primary and 

indicate the direction of the current in the secondary while 
that in the primary is decreasing. 

d. Are the currents in the primary and secondary continuous or 

alternating? 

497. a. In the di-phase alternator represented in Fig. 28, the windings 

of the coils A and B are separate. Assume direction of rota- 
tion of the armature and indicate direction of the E. M. F. 
in the various coils. 



c. 




Fig. 28. 

By means of brushes, connect an external circuit to each phase. 
Place in each circuit a step-down transformer. In the second- 
ary of one place incandescent lamps in parallel; in the 
secondary of the other place arc lights in series. 

Each primary carries 2 amperes at 2,500 volts. Each incan- 
descent lamp requires 1 ampere at 100 volts and each arc 
light requires 10 amperes at 50 volts. Neglecting loss of 
power, now many lights of each kind can be run? 



83 

CHAPTER 45. 

498. a. Make a diagram of a bipolar ring- wound A. C. generator of 12 
coils. Tap the winding at three equidistant points and 
attach the tapping wires to collector rings. Assume direction 
of rotation and indicate instantaneous direction of E. M. F. 
in the tapping wires. 

&. Draw current from the collector rings by means of brushes and 
leads and carry this current to the ring-wound field of an 
induction motor, also of 12 coils. 

c. Explain how by means of this arrangement a rotating field 
may be produced in the motor. 



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